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393 relations: A* search algorithm, ABS methods, Active set method, AdaBoost, Affine scaling, AIMMS, Alan J. Goldman, Algebraic statistics, Algorithm, Algorithm selection, Algorithmica, AMPL, APMonitor, APOPT, Approximate Competitive Equilibrium from Equal Incomes, Approximation algorithm, Aquaculture of salmonids, Argonne National Laboratory, Assignment problem, Association scheme, Balanced matrix, Balinski's theorem, Basic solution (linear programming), Benders decomposition, Benson's algorithm (Go), Big M method, Binary constraint, BIP, Bland's rule, Blossom algorithm, Boolean satisfiability problem, Bounding sphere, Branch and bound, Branch and cut, Branch and price, Bregman method, Business mathematics, Carlos Slim, Center for Operations Research and Econometrics, CER-12, Channel coordination, Chebyshev center, Circulation problem, Clock skew, COBYLA, Codimension, COIN-OR, Collision detection, Column generation, Combinatorial optimization, ..., Commercial vehicle operation, Complementarity theory, Compressed sensing, Computational geometry, Computational science, Computerized adaptive testing, Conic optimization, Constrained optimization, Constraint (mathematics), Convex analysis, Convex geometry, Convex optimization, Convex polytope, Corner case, Couenne, Covering problems, CPLEX, Crew scheduling, Criss-cross algorithm, Criticisms of neoclassical economics, Cunningham's Rule, Cut (graph theory), CUTEr, Cutting stock problem, Cutting-plane method, Dantzig–Wolfe decomposition, Data envelopment analysis, Dave Bayer, David Gale, David Shmoys, Deaths in May 2005, Decision problem, Deterministic global optimization, DICE model, Dijkstra's algorithm, Discontinuity layout optimization, Discrete geometry, Discrete mathematics, Donald Knuth, Drift plus penalty, Duality (mathematics), Duality (optimization), Dynamic programming, E. C. Rhodes, Economics, Edge coloring, Egon Balas, Egon Zakrajšek, Ehrhart polynomial, Ellipsoid method, Emilio Spedicato, Emo Welzl, Energy modeling, Engineering economics, Enterprise optimization, Extended Mathematical Programming (EMP), Facility location problem, Farkas' lemma, Feasible region, Feature selection, FICO Xpress, Flux balance analysis, FORPLAN, FortMP, FortSP, Fourier–Motzkin elimination, Fractional coloring, Fractional graph isomorphism, Frank–Wolfe algorithm, Friedrich von Wieser, Fulkerson Prize, Fundamental theorem of linear programming, Gadget (computer science), Galahad library, GAUSS (software), Gekko (optimization software), General Algebraic Modeling System, George Dantzig, George Nemhauser, Gil Kalai, Gittins index, Global optimization, GNU Linear Programming Kit, Goal programming, Goofspiel, Gurobi, Gustav S. Christensen, Harold Pender Award, Held–Karp algorithm, Hill climbing, Hirsch conjecture, History of economic thought, Hua Luogeng, Hydrological optimization, IBM 1130, Ideation (creative process), Igor Ashmanov, ILOG, Imaging spectroscopy, Info-gap decision theory, Integer points in convex polyhedra, Integer programming, Integer set library, Interior-point method, IPOPT, Iteratively reweighted least squares, Ivar Ekeland, Jack Edmonds, Jeremy Stone, Jerome Cornfield, Jewish culture, John von Neumann, John von Neumann Theory Prize, K-approximation of k-hitting set, Kantorovich inequality, Karmarkar's algorithm, Kenneth L. Clarkson, Kepler conjecture, Klee–Minty cube, Lagrangian relaxation, Layered graph drawing, Least absolute deviations, Least-squares spectral analysis, LEMON (C++ library), Lenstra–Lenstra–Lovász lattice basis reduction algorithm, Leonid Kantorovich, Leonid Khachiyan, LINDO, Linear (disambiguation), Linear algebra, Linear genetic programming, Linear production game, Linear programming decoding, Linear programming formulation, Linear programming relaxation, Linear-fractional programming, Linearity, LINGO (mathematical modeling language), List of academic fields, List of agnostics, List of algorithms, List of computer scientists, List of convexity topics, List of important publications in mathematics, List of important publications in theoretical computer science, List of lemmas, List of matrices, List of MeSH codes (L01), List of multiple discoveries, List of numerical analysis topics, List of optimization software, List of Russian IT developers, List of Russian mathematicians, List of Russian people, List of Russian scientists, List of Stanford University people, List of systems scientists, List of terms relating to algorithms and data structures, List of University of California, Berkeley alumni, List of University of California, Berkeley alumni in science and technology, List of University of Michigan alumni, LP, LP-type problem, LPBoost, Lyapunov optimization, M-matrix, Manifold regularization, Marginal conditional stochastic dominance, Marguerite Frank, Markov decision process, Martin Beale, Mathematical economics, Mathematical optimization, Matroid minor, Max-flow min-cut theorem, Maximal lotteries, Maximum coverage problem, Maximum flow problem, Maximum satisfiability problem, Möbius ladder, Mehrotra predictor–corrector method, Metabolic network modelling, Michel Balinski, Michel Deza, MIDACO, Minimum degree algorithm, Minimum-cost flow problem, MINTO, MIP, Modular Mining Systems, Moore method, Moscow Institute of Physics and Technology, Moving horizon estimation, MPS (format), Multi-commodity flow problem, Multi-objective linear programming, Multi-objective optimization, Multi-surface method, Multidisciplinary design optimization, Multipath routing, Multiplicative weight update method, Munish Chander Puri, Narendra Karmarkar, National Forest Management Act of 1976, Naum Z. Shor, Neoclassical economics, NEOS Server, Nikolaus Hofreiter, Nikolay Fedorenko, Nl (format), Nonlinear programming, Nullspace property, Numerical analysis, Open energy system models, Operations management, Operations research, Optimization Toolbox, OptimJ, Oriented matroid, Outline of academic disciplines, Outline of finance, Outline of science, P (complexity), P versus NP problem, P-complete, Paris Kanellakis Award, Paul Tseng, Perfect graph, Philip Wolfe (mathematician), Pinch analysis, Planted motif search, Policy capturing, Polyhedral combinatorics, Polyhedron, Polytope, Portfolio optimization, Power system simulation, Power-flow study, Pricing science, Project production management, Protein design, Prune and search, Pseudoconvex function, Pseudoforest, Qoca, Quadratic knapsack problem, Quadratic programming, Quadratically constrained quadratic program, Quantile regression, Radhia Cousot, Raimund Seidel, Ralph E. Gomory, RAND Corporation, Randomised decision rule, Randomized rounding, Rayleigh quotient, Reachability problem, Reasoning system, Reduced cost, Relaxation (approximation), Relaxation (iterative method), Rental harmony, Retiming, Revenue management, Revised simplex method, Richard A. Tapia, Richard Stockbridge, Robert G. Bland, Robert J. Vanderbei, Robert Solow, Robust optimization, Ron Shamir, Routing and wavelength assignment, Satisfiability, Schedule, SCIP (optimization software), SEAC (computer), Search-based software engineering, Second-order cone programming, Selmer M. Johnson, Semidefinite programming, Sequential linear-quadratic programming, Sergei Nikolaevich Chernikov, Set cover problem, Set estimation, Set packing, Shadow price, Shapley–Folkman lemma, Shortest path problem, Simon Kuznets, Simplex, Simplex algorithm, Simulation-based optimization, Slack variable, Smale's problems, Smallest-circle problem, Smart market, Socialist calculation debate, Software development effort estimation, Software patent, Soviet-type economic planning, Sparse approximation, Sridhar Tayur, Star-shaped polygon, Steven J. Miller, Stigler diet, Stochastic programming, Strong duality, Theodore Motzkin, Theory of constraints, Theory of two-level planning, Thomas L. Saaty, Time complexity, Tixati, Tobias Dantzig, TOMLAB, TOMNET, TomSym, Total dual integrality, Trajectory optimization, Transportation theory (mathematics), Travelling salesman problem, Unimodular matrix, Unique sink orientation, Utility maximization problem, Variable neighborhood search, Václav Chvátal, Vertex cover, Victor Klee, Victor Zalgaller, Wald's maximin model, Weak duality, Weak ordering, William W. Cooper, Workflow, Workforce modeling, Yield curve, Yinyu Ye, Zadeh's Rule, Zero-sum game, Zionts–Wallenius method, 1947 in science, 1965 Soviet economic reform. Expand index (343 more) »
A* search algorithm
In computer science, A* (pronounced as "A star") is a computer algorithm that is widely used in pathfinding and graph traversal, which is the process of plotting an efficiently directed path between multiple points, called "nodes".
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ABS methods
ABS methods, where the acronym contains the initials of Jozsef Abaffy, Charles G. Broyden and Emilio Spedicato, have been developed since 1981 to generate a large class of algorithms for the following applications.
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Active set method
In mathematical optimization, a problem is defined using an objective function to minimize or maximize, and a set of constraints that define the feasible region, that is, the set of all x to search for the optimal solution.
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AdaBoost
AdaBoost, short for Adaptive Boosting, is a machine learning meta-algorithm formulated by Yoav Freund and Robert Schapire, who won the 2003 Gödel Prize for their work.
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Affine scaling
In mathematical optimization, affine scaling is an algorithm for solving linear programming problems.
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AIMMS
is a prescriptive analytics software company with offices in the Netherlands, United States, China and Singapore.
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Alan J. Goldman
Alan J. Goldman (1932–2010) was an American expert in operations research.
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Algebraic statistics
Algebraic statistics is the use of algebra to advance statistics.
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Algorithm
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.
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Algorithm selection
Algorithm selection (sometimes also called per-instance algorithm selection or offline algorithm selection) is a meta-algorithmic technique to choose an algorithm from a portfolio on an instance-by-instance basis.
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Algorithmica
Algorithmica is a monthly peer reviewed, scientific journal, published by Springer Science+Business Media focused on research and application of computer science algorithms.
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AMPL
A Mathematical Programming Language (AMPL) is an algebraic modeling language to describe and solve high-complexity problems for large-scale mathematical computing (i.e., large-scale optimization and scheduling-type problems).
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APMonitor
Advanced process monitor (APMonitor), is a modeling language for differential algebraic (DAE) equations.
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APOPT
APOPT (for Advanced Process OPTimizer) is a software package for solving large-scale optimization problems of any of these forms.
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Approximate Competitive Equilibrium from Equal Incomes
Approximate Competitive Equilibrium from Equal Incomes (A-CEEI) is a procedure for fair item assignment.
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Approximation algorithm
In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to NP-hard optimization problems with provable guarantees on the distance of the returned solution to the optimal one.
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Aquaculture of salmonids
The aquaculture of salmonids is the farming and harvesting of salmonids under controlled conditions for both commercial and recreational purposes.
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Argonne National Laboratory
Argonne National Laboratory is a science and engineering research national laboratory operated by the University of Chicago Argonne LLC for the United States Department of Energy located near Lemont, Illinois, outside Chicago.
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Assignment problem
The assignment problem is one of the fundamental combinatorial optimization problems in the branch of optimization or operations research in mathematics.
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Association scheme
The theory of association schemes arose in statistics, in the theory of experimental design for the analysis of variance.
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Balanced matrix
In mathematics, a balanced matrix is a 0-1 matrix (a matrix where every entry is either zero or one) that does not contain any square submatrix of odd order having all row sums and all column sums equal to 2.
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Balinski's theorem
In polyhedral combinatorics, a branch of mathematics, Balinski's theorem is a statement about the graph-theoretic structure of three-dimensional polyhedra and higher-dimensional polytopes.
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Basic solution (linear programming)
In linear programming, a discipline within applied mathematics, a basic solution is any solution of a linear programming problem satisfying certain specified technical conditions.
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Benders decomposition
Benders decomposition (or Benders' decomposition) is a technique in mathematical programming that allows the solution of very large linear programming problems that have a special block structure.
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Benson's algorithm (Go)
In the game Go, Benson's algorithm (named after David B. Benson) can be used to determine the stones which are safe from capture no matter how many turns in a row the opposing player gets, i.e. unconditionally alive.
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Big M method
In operations research, the Big M method is a method of solving linear programming problems using the simplex algorithm.
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Binary constraint
A binary constraint, in mathematical optimization, is a constraint that involves exactly two variables.
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BIP
Bip or BIP may refer to.
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Bland's rule
In mathematical optimization, Bland's rule (also known as Bland's algorithm or Bland's anti-cycling rule) is an algorithmic refinement of the simplex method for linear optimization.
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Blossom algorithm
The blossom algorithm is an algorithm in graph theory for constructing maximum matchings on graphs.
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Boolean satisfiability problem
In computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated as SATISFIABILITY or SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula.
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Bounding sphere
In mathematics, given a non-empty set of objects of finite extension in n-dimensional space, for example a set of points, a bounding sphere, enclosing sphere or enclosing ball for that set is an n-dimensional solid sphere containing all of these objects.
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Branch and bound
Branch and bound (BB, B&B, or BnB) is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization.
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Branch and cut
Branch and cut is a method of combinatorial optimization for solving integer linear programs (ILPs), that is, linear programming (LP) problems where some or all the unknowns are restricted to integer values.
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Branch and price
In applied mathematics, branch and price is a method of combinatorial optimization for solving integer linear programming (ILP) and mixed integer linear programming (MILP) problems with many variables.
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Bregman method
Bregman's method is an iterative algorithm to solve certain convex optimization problems.
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Business mathematics
Business mathematics is mathematics used by commercial enterprises to record and manage business operations.
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Carlos Slim
Carlos Slim Helú (born January 28, 1940) is a Mexican business magnate, engineer, investor and philanthropist.
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Center for Operations Research and Econometrics
The Center for Operations Research and Econometrics (CORE) is an interdisciplinary research institute of the Université catholique de Louvain (UCL) located in Louvain-la-Neuve, Belgium.
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CER-12
CER (– Digital Electronic Computer) model 12 was a third-generation digital computer developed by Mihajlo Pupin Institute (Serbia) in 1971 and intended for "business and statistical data processing" (see ref. Lit. #1 and #4).
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Channel coordination
Channel coordination (or supply chain coordination) aims at improving supply chain performance by aligning the plans and the objectives of individual enterprises.
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Chebyshev center
In geometry, the Chebyshev center of a bounded set Q having non-empty interior is the center of the minimal-radius ball enclosing the entire set Q, or alternatively (and non-equivalently) the center of largest inscribed ball of Q. In the field of parameter estimation, the Chebyshev center approach tries to find an estimator \hat x for x given the feasibility set Q, such that \hat x minimizes the worst possible estimation error for x (e.g. best worst case).
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Circulation problem
The circulation problem and its variants are a generalisation of network flow problems, with the added constraint of a lower bound on edge flows, and with flow conservation also being required for the source and sink (i.e. there are no special nodes).
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Clock skew
Clock skew (sometimes called timing skew) is a phenomenon in synchronous digital circuit systems (such as computer systems) in which the same sourced clock signal arrives at different components at different times i.e. the instantaneous difference between the readings of any two clocks is called their skew.
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COBYLA
Constrained optimization by linear approximation (COBYLA) is a numerical optimization method for constrained problems where the derivative of the objective function is not known, invented by Michael J. D. Powell.
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Codimension
In mathematics, codimension is a basic geometric idea that applies to subspaces in vector spaces, to submanifolds in manifolds, and suitable subsets of algebraic varieties.
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COIN-OR
Computational Infrastructure for Operations Research (COIN-OR), is a project that aims to "create for mathematical software what the open literature is for mathematical theory." The open literature (e.g., a research journal) provides the operations research (OR) community with a peer-review process and an archive.
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Collision detection
Collision detection is the computational problem of detecting the intersection of two or more objects.
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Column generation
Column generation or delayed column generation is an efficient algorithm for solving larger linear programs.
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Combinatorial optimization
In applied mathematics and theoretical computer science, combinatorial optimization is a topic that consists of finding an optimal object from a finite set of objects.
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Commercial vehicle operation
Commercial Vehicle Operations is an application of Intelligent Transportation Systems for trucks.
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Complementarity theory
A complementarity problem is a type of mathematical optimization problem.
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Compressed sensing
Compressed sensing (also known as compressive sensing, compressive sampling, or sparse sampling) is a signal processing technique for efficiently acquiring and reconstructing a signal, by finding solutions to underdetermined linear systems.
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Computational geometry
Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry.
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Computational science
Computational science (also scientific computing or scientific computation (SC)) is a rapidly growing multidisciplinary field that uses advanced computing capabilities to understand and solve complex problems.
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Computerized adaptive testing
Computerized adaptive testing (CAT) is a form of computer-based test that adapts to the examinee's ability level.
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Conic optimization
Conic optimization is a subfield of convex optimization that studies problems consisting of minimizing a convex function over the intersection of an affine subspace and a convex cone.
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Constrained optimization
In mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function with respect to some variables in the presence of constraints on those variables.
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Constraint (mathematics)
In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy.
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Convex analysis
Convex analysis is the branch of mathematics devoted to the study of properties of convex functions and convex sets, often with applications in convex minimization, a subdomain of optimization theory.
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Convex geometry
In mathematics, convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space.
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Convex optimization
Convex optimization is a subfield of optimization that studies the problem of minimizing convex functions over convex sets.
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Convex polytope
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn.
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Corner case
In engineering, a corner case (or pathological case) involves a problem or situation that occurs only outside of normal operating parameters—specifically one that manifests itself when multiple environmental variables or conditions are simultaneously at extreme levels, even though each parameter is within the specified range for that parameter.
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Couenne
Convex Over and Under ENvelopes for Nonlinear Estimation (Couenne) is an open source library for solving global optimization problems, also termed mixed integer nonlinear optimization problems.
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Covering problems
In combinatorics and computer science, covering problems are computational problems that ask whether a certain combinatorial structure 'covers' another, or how large the structure has to be to do that.
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CPLEX
IBM ILOG CPLEX Optimization Studio (often informally referred to simply as CPLEX) is an optimization software package.
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Crew scheduling
Crew scheduling is the process of assigning crews to operate transportation systems, such as rail lines or airlines.
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Criss-cross algorithm
In mathematical optimization, the criss-cross algorithm is any of a family of algorithms for linear programming.
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Criticisms of neoclassical economics
Neo-classical economics has come under critique on the basis of its core ideologies, assumptions, and other matters.
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Cunningham's Rule
In mathematical optimization, Cunningham's rule (also known as least recently considered rule or round-robin rule) is an algorithmic refinement of the simplex method for linear optimization.
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Cut (graph theory)
In graph theory, a cut is a partition of the vertices of a graph into two disjoint subsets.
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CUTEr
CUTEr (Constrained and Unconstrained Testing Environment, revisited) is an open source testing environment for optimization and linear algebra solvers.
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Cutting stock problem
In operations research, the cutting-stock problem is the problem of cutting standard-sized pieces of stock material, such as paper rolls or sheet metal, into pieces of specified sizes while minimizing material wasted.
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Cutting-plane method
In mathematical optimization, the cutting-plane method is any of a variety of optimization methods that iteratively refine a feasible set or objective function by means of linear inequalities, termed cuts.
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Dantzig–Wolfe decomposition
Dantzig–Wolfe decomposition is an algorithm for solving linear programming problems with special structure.
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Data envelopment analysis
Data envelopment analysis (DEA) is a nonparametric method in operations research and economics for the estimation of production frontiers.
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Dave Bayer
David Allen Bayer (born November 29, 1955) is an American mathematician known for his contributions in algebra and symbolic computation and for his consulting work in the movie industry.
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David Gale
David Gale (December 13, 1921 – March 7, 2008) was an American mathematician and economist.
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David Shmoys
David Bernard Shmoys (born 1959) is a Professor in the School of Operations Research and Information Engineering and the Department of Computer Science at Cornell University.
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Deaths in May 2005
The following is a list of notable people who died in May 2005.
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Decision problem
In computability theory and computational complexity theory, a decision problem is a problem that can be posed as a yes-no question of the input values.
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Deterministic global optimization
Deterministic global optimization is a branch of numerical optimization which focuses on finding the global solutions of an optimization problem whilst providing theoretical guarantees that the reported solution is indeed the global one, within some predefined tolerance.
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DICE model
The Dynamic Integrated Climate-Economy model, referred to as the DICE model or Dice model, is a computer-based integrated assessment model developed by William Nordhaus that “integrates in an end-to-end fashion the economics, carbon cycle, climate science, and impacts in a highly aggregated model that allows a weighing of the costs and benefits of taking steps to slow greenhouse warming." Nordhaus also developed the RICE model (Regional Integrated Climate-Economy model), a variant of the DICE model that was updated and developed alongside the DICE model.
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Dijkstra's algorithm
Dijkstra's algorithm is an algorithm for finding the shortest paths between nodes in a graph, which may represent, for example, road networks.
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Discontinuity layout optimization
Discontinuity layout optimization (DLO) is an engineering analysis procedure which can be used to directly establish the amount of load that can be carried by a solid or structure prior to collapse.
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Discrete geometry
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects.
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Discrete mathematics
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.
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Donald Knuth
Donald Ervin Knuth (born January 10, 1938) is an American computer scientist, mathematician, and professor emeritus at Stanford University.
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Drift plus penalty
In the mathematical theory of probability, the drift-plus-penalty method is used for optimization of queueing networks and other stochastic systems.
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Duality (mathematics)
In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of A is B, then the dual of B is A. Such involutions sometimes have fixed points, so that the dual of A is A itself.
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Duality (optimization)
In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem.
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Dynamic programming
Dynamic programming is both a mathematical optimization method and a computer programming method.
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E. C. Rhodes
Edmund Cecil Rhodes (1892–1964), a statistician, was born in Yorkshire and named after Cecil Rhodes.
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Economics
Economics is the social science that studies the production, distribution, and consumption of goods and services.
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Edge coloring
In graph theory, an edge coloring of a graph is an assignment of "colors" to the edges of the graph so that no two adjacent edges have the same color.
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Egon Balas
Egon Balas (Cluj, Romania, June 7, 1922) is an applied mathematician and a professor of industrial administration and applied mathematics at Carnegie Mellon University.
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Egon Zakrajšek
Egon Zakrajšek (July 7, 1941 – September 2002) was a Slovene mathematician and computer scientist.
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Ehrhart polynomial
In mathematics, an integral polytope has an associated Ehrhart polynomial that encodes the relationship between the volume of a polytope and the number of integer points the polytope contains.
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Ellipsoid method
In mathematical optimization, the ellipsoid method is an iterative method for minimizing convex functions.
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Emilio Spedicato
Emilio Spedicato (born 1945) is full professor of operations research at the University of Bergamo in Italy.
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Emo Welzl
Emmerich (Emo) Welzl (born 4 August 1958 in Linz, Austria), retrieved 2012-02-11.
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Energy modeling
Energy modeling or energy system modeling is the process of building computer models of energy systems in order to analyze them.
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Engineering economics
Engineering Economics, previously known as engineering economy, is a subset of economics concerned with the use and "...application of economic principles" Dharmaraj, E..
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Enterprise optimization
Enterprise Optimization (EO) is "a systematic process of planning, integrating, coordinating and executing all dimensions of enterprise activities for best-possible mission-focused results".
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Extended Mathematical Programming (EMP)
Algebraic modeling languages like AIMMS, AMPL, GAMS, MPL and others have been developed to facilitate the description of a problem in mathematical terms and to link the abstract formulation with data-management systems on the one hand and appropriate algorithms for solution on the other.
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Facility location problem
The study of facility location problems, also known as location analysis, is a branch of operations research and computational geometry concerned with the optimal placement of facilities to minimize transportation costs while considering factors like avoiding placing hazardous materials near housing, and competitors' facilities.
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Farkas' lemma
Farkas' lemma is a solvability theorem for a finite system of linear inequalities in mathematics.
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Feasible region
In mathematical optimization, a feasible region, feasible set, search space, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints.
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Feature selection
In machine learning and statistics, feature selection, also known as variable selection, attribute selection or variable subset selection, is the process of selecting a subset of relevant features (variables, predictors) for use in model construction.
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FICO Xpress
The FICO Xpress Optimizer is a commercial optimization solver for linear programming (LP), mixed integer linear programming (MILP), convex quadratic programming (QP), convex quadratically constrained quadratic programming (QCQP), second-order cone programming (SOCP) and their mixed integer counterparts.
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Flux balance analysis
Flux balance analysis (FBA) is a mathematical method for simulating metabolism in genome-scale reconstructions of metabolic networks.
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FORPLAN
FORPLAN, short for FORest PLANning, is a computer program developed by K. Norman Johnson and others that uses a linear programming model to estimate land management resource outputs pursuant to the National Forest Management Act of 1976.
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FortMP
FortMP is a software package for solving large-scale optimization problems.
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FortSP
FortSP is a software package for solving stochastic programming (SP) problems.
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Fourier–Motzkin elimination
Fourier–Motzkin elimination, also known as the FME method, is a mathematical algorithm for eliminating variables from a system of linear inequalities.
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Fractional coloring
Fractional coloring is a topic in a young branch of graph theory known as fractional graph theory.
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Fractional graph isomorphism
In graph theory, a fractional isomorphism of graphs whose adjacency matrices are denoted A and B is a doubly stochastic matrix D such that DA.
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Frank–Wolfe algorithm
The Frank–Wolfe algorithm is an iterative first-order optimization algorithm for constrained convex optimization.
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Friedrich von Wieser
Friedrich Freiherr von Wieser (10 July 1851 – 22 July 1926) was an early (so-called "first generation") economist of the Austrian School of economics.
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Fulkerson Prize
The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Optimization Society (MOS) and the American Mathematical Society (AMS).
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Fundamental theorem of linear programming
In mathematical optimization, the fundamental theorem of linear programming states, in a weak formulation, that the maxima and minima of a linear function over a convex polygonal region occur at the region's corners.
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Gadget (computer science)
In computational complexity theory, a gadget is a subset of a problem instance that simulates the behavior of one of the fundamental units of a different computational problem.
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Galahad library
The Galahad library is a thread-safe library of packages for the solution of optimization—or mathematical programming—problems.
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GAUSS (software)
GAUSS is a matrix programming language for mathematics and statistics, developed and marketed by Aptech Systems.
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Gekko (optimization software)
The GEKKO Python package solves mixed-integer and differential algebraic equations with nonlinear programming solvers (IPOPT, APOPT, BPOPT, SNOPT, MINOS).
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General Algebraic Modeling System
The General Algebraic Modeling System (GAMS) is a high-level modeling system for mathematical optimization.
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George Dantzig
George Bernard Dantzig (November 8, 1914 – May 13, 2005) was an American mathematical scientist who made important contributions to operations research, computer science, economics, and statistics.
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George Nemhauser
George Lann Nemhauser (born 1937).
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Gil Kalai
Gil Kalai (born 1955) is the Henry and Manya Noskwith Professor of Mathematics at the Hebrew University of Jerusalem, and adjunct professor of mathematics and of computer science at Yale University.
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Gittins index
The Gittins index is a measure of the reward that can be achieved by a random process bearing a termination state and evolving from its present state onward, under the option of terminating the said process at every later stage with the accrual of the probabilistic expected reward from that stage up to the attainment of its termination state.
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Global optimization
Global optimization is a branch of applied mathematics and numerical analysis that deals with the global optimization of a function or a set of functions according to some criteria.
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GNU Linear Programming Kit
The GNU Linear Programming Kit (GLPK) is a software package intended for solving large-scale linear programming (LP), mixed integer programming (MIP), and other related problems.
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Goal programming
Goal programming is a branch of multiobjective optimization, which in turn is a branch of multi-criteria decision analysis (MCDA).
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Goofspiel
Goofspiel, also known as The Game of Pure Strategy or GOPS, is a card game for two or more players.
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Gurobi
The Gurobi Optimizer is a commercial optimization solver for linear programming (LP), quadratic programming (QP), quadratically constrained programming (QCP), mixed integer linear programming (MILP), mixed-integer quadratic programming (MIQP), and mixed-integer quadratically constrained programming (MIQCP).
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Gustav S. Christensen
Gustav Stroem Christensen; (born April 1, 1929 Laesoe, Denmark), was an academic mathematician and engineer.
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Harold Pender Award
The Harold Pender Award, initiated in 1972 and named after founding Dean Harold Pender, is given by the Faculty of the School of Engineering and Applied Science of the University of Pennsylvania to an outstanding member of the engineering profession who has achieved distinction by significant contributions to society.
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Held–Karp algorithm
The Held–Karp algorithm, also called Bellman–Held–Karp algorithm, is a dynamic programming algorithm proposed in 1962 independently by Bellman and by Held and Karp to solve the Traveling Salesman Problem (TSP).
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Hill climbing
In numerical analysis, hill climbing is a mathematical optimization technique which belongs to the family of local search.
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Hirsch conjecture
In mathematical programming and polyhedral combinatorics, the Hirsch conjecture is the statement that the edge-vertex graph of an n-facet polytope in d-dimensional Euclidean space has diameter no more than n − d.
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History of economic thought
The history of economic thought deals with different thinkers and theories in the subject that became political economy and economics, from the ancient world to the present day in the 21st Century.
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Hua Luogeng
Hua Luogeng, or Hua Loo-gehng (12 November 1910 – 12 June 1985), was a Chinese mathematician famous for his important contributions to number theory and for his role as the leader of mathematics research and education in the People's Republic of China.
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Hydrological optimization
Hydrological optimization applies mathematical optimization techniques (such as linear programming) to water-related problems.
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IBM 1130
The IBM 1130 Computing System, introduced in 1965, was IBM's least expensive computer at that time.
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Ideation (creative process)
Ideation is the creative process of generating, developing, and communicating new ideas, where an idea is understood as a basic element of thought that can be either visual, concrete, or abstract.
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Igor Ashmanov
Igor Stanislа́vovich Ashmа́nov (born 9 January 1962, Moscow) — Russian entrepreneur specializing in information technology, artificial intelligence, software development, project management.
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ILOG
ILOG was an international software company purchased and incorporated into IBM announced in January, 2009.
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Imaging spectroscopy
In imaging spectroscopy (also hyperspectral or spectral imaging) each pixel of an image acquires many bands of light intensity data from the spectrum, instead of just the three bands of the RGB color model.
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Info-gap decision theory
Info-gap decision theory is a non-probabilistic decision theory that seeks to optimize robustness to failure – or opportuneness for windfall – under severe uncertainty,Yakov Ben-Haim, Information-Gap Theory: Decisions Under Severe Uncertainty, Academic Press, London, 2001.
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Integer points in convex polyhedra
The study of integer points in convex polyhedra is motivated by questions such as "how many nonnegative integer-valued solutions does a system of linear equations with nonnegative coefficients have" or "how many solutions does an integer linear program have".
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Integer programming
An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers.
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Integer set library
isl (integer set library) is a portable C library for manipulating sets and relations of integer points bounded by linear constraints.
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Interior-point method
Interior-point methods (also referred to as barrier methods) are a certain class of algorithms that solve linear and nonlinear convex optimization problems.
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IPOPT
IPOPT, short for "Interior Point OPTimizer, pronounced I-P-Opt", is a software library for large scale nonlinear optimization of continuous systems.
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Iteratively reweighted least squares
The method of iteratively reweighted least squares (IRLS) is used to solve certain optimization problems with objective functions of the form: by an iterative method in which each step involves solving a weighted least squares problem of the form:C.
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Ivar Ekeland
Ivar I. Ekeland (born 2 July 1944, Paris) is a French mathematician of Norwegian descent.
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Jack Edmonds
Jack R. Edmonds (born April 5, 1934) is an American computer scientist, regarded as one of the most important contributors to the field of combinatorial optimization.
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Jeremy Stone
Jeremy J. Stone (November 23, 1935 – January 1, 2017) was president of the Federation of American Scientists from 1970 to 2000, where he led that organization's advocacy initiatives in arms control, human rights, and foreign policy.
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Jerome Cornfield
Jerome (Jerry) Cornfield (1912–1979) was a US statistician.
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Jewish culture
Jewish culture is the culture of the Jewish people from the formation of the Jewish nation in biblical times through life in the diaspora and the modern state of Israel.
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John von Neumann
John von Neumann (Neumann János Lajos,; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, and polymath.
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John von Neumann Theory Prize
The John von Neumann Theory Prize of the Institute for Operations Research and the Management Sciences (INFORMS) is awarded annually to an individual (or sometimes a group) who has made fundamental and sustained contributions to theory in operations research and the management sciences.
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K-approximation of k-hitting set
In computer science, k-approximation of k-hitting set is an approximation algorithm for weighted hitting set.
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Kantorovich inequality
In mathematics, the Kantorovich inequality is a particular case of the Cauchy–Schwarz inequality, which is itself a generalization of the triangle inequality.
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Karmarkar's algorithm
Karmarkar's algorithm is an algorithm introduced by Narendra Karmarkar in 1984 for solving linear programming problems.
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Kenneth L. Clarkson
Kenneth Lee Clarkson is an American computer scientist known for his research in computational geometry.
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Kepler conjecture
The Kepler conjecture, named after the 17th-century mathematician and astronomer Johannes Kepler, is a mathematical theorem about sphere packing in three-dimensional Euclidean space.
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Klee–Minty cube
The Klee–Minty cube or Klee–Minty polytope (named after Victor Klee and) is a unit hypercube of variable dimension whose corners have been perturbed.
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Lagrangian relaxation
In the field of mathematical optimization, Lagrangian relaxation is a relaxation method which approximates a difficult problem of constrained optimization by a simpler problem.
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Layered graph drawing
Layered graph drawing or hierarchical graph drawing is a type of graph drawing in which the vertices of a directed graph are drawn in horizontal rows or layers with the edges generally directed downwards.
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Least absolute deviations
Least absolute deviations (LAD), also known as least absolute errors (LAE), least absolute value (LAV), least absolute residual (LAR), sum of absolute deviations, or the ''L''1 norm condition, is a statistical optimality criterion and the statistical optimization technique that relies on it.
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Least-squares spectral analysis
Least-squares spectral analysis (LSSA) is a method of estimating a frequency spectrum, based on a least squares fit of sinusoids to data samples, similar to Fourier analysis.
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LEMON (C++ library)
LEMON is an open source graph library written in the C++ language providing implementations of common data structures and algorithms with focus on combinatorial optimization tasks connected mainly with graphs and networks.
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Lenstra–Lenstra–Lovász lattice basis reduction algorithm
The Lenstra–Lenstra–Lovász (LLL) lattice basis reduction algorithm is a polynomial time lattice reduction algorithm invented by Arjen Lenstra, Hendrik Lenstra and László Lovász in 1982.
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Leonid Kantorovich
Leonid Vitaliyevich Kantorovich (a) (19 January 19127 April 1986) was a Soviet mathematician and economist, known for his theory and development of techniques for the optimal allocation of resources.
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Leonid Khachiyan
Leonid Genrikhovich Khachiyan (Լեոնիդ Գենրիխովիչ Խաչիյան; Леонид Генрихович Хачиян; May 3, 1952 – April 29, 2005) was a Soviet mathematician of Armenian descent who taught Computer Science at Rutgers University.
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LINDO
LINDO (Linear, Interactive, and Discrete Optimizer) is a software package for linear programming, integer programming, nonlinear programming, stochastic programming and global optimization.
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Linear (disambiguation)
The word linear comes from the Latin word linearis, which means "created by lines".
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Linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.
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Linear genetic programming
Linear genetic programming (LGP) is a particular subset of genetic programming wherein computer programs in a population are represented as a sequence of instructions from imperative programming language or machine language.
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Linear production game
Linear Production Game (LP Game) is a N-person game in which the value of a coalition can be obtained by solving a Linear Programming problem.
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Linear programming decoding
In information theory and coding theory, linear programming decoding (LP decoding) is a decoding method which uses concepts from linear programming (LP) theory to solve decoding problems.
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Linear programming formulation
Linear programming formulation is the applied methodology to express a real problem or phenomenon in terms of linear inequalities, thus stating it as a linear programming problem.
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Linear programming relaxation
In mathematics, the relaxation of a (mixed) integer linear program is the problem that arises by removing the integrality constraint of each variable.
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Linear-fractional programming
In mathematical optimization, linear-fractional programming (LFP) is a generalization of linear programming (LP).
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Linearity
Linearity is the property of a mathematical relationship or function which means that it can be graphically represented as a straight line.
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LINGO (mathematical modeling language)
LINGO is a mathematical modeling language designed for formulating and solving optimization problems, including linear, integer, and nonlinear programming problems.
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List of academic fields
The following outline is provided as an overview of an topical guide to academic disciplines: An academic discipline or field of study is known as a branch of knowledge.
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List of agnostics
Listed here are persons who have identified themselves as theologically agnostic.
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List of algorithms
The following is a list of algorithms along with one-line descriptions for each.
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List of computer scientists
This is a list of computer scientists, people who do work in computer science, in particular researchers and authors.
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List of convexity topics
This is a list of convexity topics, by Wikipedia page.
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List of important publications in mathematics
This is a list of important publications in mathematics, organized by field.
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List of important publications in theoretical computer science
This is a list of important publications in theoretical computer science, organized by field.
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List of lemmas
This following is a list of lemmas (or, "lemmata", i.e. minor theorems, or sometimes intermediate technical results factored out of proofs).
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List of matrices
This page lists some important classes of matrices used in mathematics, science and engineering.
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List of MeSH codes (L01)
The following is a list of the "L" codes for MeSH.
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List of multiple discoveries
Historians and sociologists have remarked the occurrence, in science, of "multiple independent discovery".
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List of numerical analysis topics
This is a list of numerical analysis topics.
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List of optimization software
Given a transformation between input and output values, described by a mathematical function f, optimization deals with generating and selecting a best solution from some set of available alternatives, by systematically choosing input values from within an allowed set, computing the output of the function, and recording the best output values found during the process.
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List of Russian IT developers
This list of Russian IT developers includes the hardware engineers, computer scientists and programmers from the Russian Empire, the Soviet Union and the Russian Federation.
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List of Russian mathematicians
This list of Russian mathematicians includes the famous mathematicians from the Russian Empire, the Soviet Union and the Russian Federation.
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List of Russian people
This is a list of people associated with the modern Russian Federation, the Soviet Union, Imperial Russia, Russian Tsardom, the Grand Duchy of Moscow, and other predecessor states of Russia.
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List of Russian scientists
Alona Soschen.
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List of Stanford University people
This page lists the members of Stanford University, including students, alumni, faculty and academic affiliates associated.
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List of systems scientists
This is a list of systems scientists, people who made notable contributions in the field of the systems sciences.
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List of terms relating to algorithms and data structures
The NIST Dictionary of Algorithms and Data Structures is a reference work maintained by the U.S. National Institute of Standards and Technology.
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List of University of California, Berkeley alumni
This page lists notable alumni and students of the University of California, Berkeley.
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List of University of California, Berkeley alumni in science and technology
This page lists notable alumni and students of the University of California, Berkeley.
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List of University of Michigan alumni
There are more than 500,000 living alumni of the University of Michigan.
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LP
LP or lp may stand for.
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LP-type problem
In the study of algorithms, an LP-type problem (also called a generalized linear program) is an optimization problem that shares certain properties with low-dimensional linear programs and that may be solved by similar algorithms.
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LPBoost
Linear Programming Boosting (LPBoost) is a supervised classifier from the boosting family of classifiers.
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Lyapunov optimization
This article describes Lyapunov optimization for dynamical systems.
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M-matrix
In mathematics, especially linear algebra, an M-matrix is a ''Z''-matrix with eigenvalues whose real parts are nonnegative.
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Manifold regularization
In machine learning, Manifold regularization is a technique for using the shape of a dataset to constrain the functions that should be learned on that dataset.
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Marginal conditional stochastic dominance
In finance, marginal conditional stochastic dominance is a condition under which a portfolio can be improved in the eyes of all risk-averse investors by incrementally moving funds out of one asset (or one sub-group of the portfolio's assets) and into another.
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Marguerite Frank
Marguerite Straus Frank (born September 8, 1927) is an American-French mathematician who is a pioneer in convex optimization theory and mathematical programming.
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Markov decision process
Markov decision processes (MDPs) provide a mathematical framework for modeling decision making in situations where outcomes are partly random and partly under the control of a decision maker.
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Martin Beale
Evelyn Martin Lansdowne Beale FRS (8 September 1928 – 23 December 1985) was an applied mathematician and statistician who was one of the pioneers of mathematical programming.
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Mathematical economics
Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics.
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Mathematical optimization
In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of available alternatives.
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Matroid minor
In the mathematical theory of matroids, a minor of a matroid M is another matroid N that is obtained from M by a sequence of restriction and contraction operations.
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Max-flow min-cut theorem
In computer science and optimization theory, the max-flow min-cut theorem states that in a flow network, the maximum amount of flow passing from the ''source'' to the ''sink'' is equal to the total weight of the edges in the minimum cut, i.e. the smallest total weight of the edges which if removed would disconnect the source from the sink.
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Maximal lotteries
Maximal lotteries refers to a probabilistic voting system first considered by Germain KrewerasG.
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Maximum coverage problem
The maximum coverage problem is a classical question in computer science, computational complexity theory, and operations research.
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Maximum flow problem
In optimization theory, maximum flow problems involve finding a feasible flow through a single-source, single-sink flow network that is maximum.
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Maximum satisfiability problem
In computational complexity theory, the maximum satisfiability problem (MAX-SAT) is the problem of determining the maximum number of clauses, of a given Boolean formula in conjunctive normal form, that can be made true by an assignment of truth values to the variables of the formula.
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Möbius ladder
In graph theory, the Möbius ladder Mn is a cubic circulant graph with an even number n of vertices, formed from an n-cycle by adding edges (called "rungs") connecting opposite pairs of vertices in the cycle.
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Mehrotra predictor–corrector method
Mehrotra's predictor–corrector method in optimization is a specific interior point method for linear programming.
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Metabolic network modelling
Metabolic network reconstruction and simulation allows for an in-depth insight into the molecular mechanisms of a particular organism.
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Michel Balinski
Michel Louis Balinski (born October 6, 1933) is an applied mathematician, economist, operations research analyst and political scientist.
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Michel Deza
Michel Marie Deza (27 April 1939.-23 November 2016) was a Soviet and French mathematician, specializing in combinatorics, discrete geometry and graph theory.
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MIDACO
MIDACO (Mixed Integer Distributed Ant Colony Optimization) is a software package for numerical optimization based on evolutionary computing.
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Minimum degree algorithm
In numerical analysis the minimum degree algorithm is an algorithm used to permute the rows and columns of a symmetric sparse matrix before applying the Cholesky decomposition, to reduce the number of non-zeros in the Cholesky factor.
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Minimum-cost flow problem
The minimum-cost flow problem (MCFP) is an optimization and decision problem to find the cheapest possible way of sending a certain amount of flow through a flow network.
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MINTO
MINTO (Mixed Integer Optimizer) is an integer programming solver which uses branch and bound algorithm.
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MIP
MIP may refer to.
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Modular Mining Systems
Modular Mining Systems, Inc. (Modular), headquartered in Tucson, Arizona, U.S.A., is a privately held company that develops, manufactures, markets, and services mining equipment management systems.
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Moore method
The Moore method is a deductive manner of instruction used in advanced mathematics courses.
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Moscow Institute of Physics and Technology
Moscow Institute of Physics and Technology (Московский Физико-Технический институт), known informally as PhysTech (Физтех), is a Russian university, originally established in Soviet Union.
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Moving horizon estimation
Moving horizon estimation (MHE) is an optimization approach that uses a series of measurements observed over time, containing noise (random variations) and other inaccuracies, and produces estimates of unknown variables or parameters.
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MPS (format)
MPS (Mathematical Programming System) is a file format for presenting and archiving linear programming (LP) and mixed integer programming problems.
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Multi-commodity flow problem
The multi-commodity flow problem is a network flow problem with multiple commodities (flow demands) between different source and sink nodes.
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Multi-objective linear programming
Multi-objective linear programming is a subarea of mathematical optimization.
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Multi-objective optimization
Multi-objective optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, multiattribute optimization or Pareto optimization) is an area of multiple criteria decision making, that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously.
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Multi-surface method
The multi-surface method (MSM) is a form of decision making using the concept of piecewise-linear separability of datasets to categorize data.
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Multidisciplinary design optimization
Multi-disciplinary design optimization (MDO) is a field of engineering that uses optimization methods to solve design problems incorporating a number of disciplines.
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Multipath routing
Multipath routing is the routing technique of using multiple alternative paths through a network, which can yield a variety of benefits such as fault tolerance, increased bandwidth, or improved security.
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Multiplicative weight update method
Multiplicative weight update method is a meta-algorithm.
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Munish Chander Puri
Munish Chander Puri (15 August 1939 – 28 December 2005) was Professor Emeritus of Mathematics at IIT Delhi.
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Narendra Karmarkar
Narendra Krishna Karmarkar (born 1957) is an Indian mathematician, who developed Karmarkar's algorithm.
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National Forest Management Act of 1976
The National Forest Management Act (NFMA) of 1976 (P.L. 94-588) is a United States federal law that is the primary statute governing the administration of national forests and was an amendment to the Forest and Rangeland Renewable Resources Planning Act of 1974, which called for the management of renewable resources on national forest lands.
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Naum Z. Shor
Naum Zuselevich Shor (Наум Зуселевич Шор) (1 January 1937 – 26 February 2006) was a Soviet and Ukrainian Jewish mathematician specializing in optimization.
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Neoclassical economics
Neoclassical economics is an approach to economics focusing on the determination of goods, outputs, and income distributions in markets through supply and demand.
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NEOS Server
The NEOS Server is an Internet-based client-server application that provides free access to a library of optimization solvers.
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Nikolaus Hofreiter
Nikolaus Hofreiter (8 May 1904 – 23 January 1990) was an Austrian mathematician who worked mainly in number theory.
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Nikolay Fedorenko
Nikolay Prokofyevich Fedorenko (Никола́й Проко́фьевич Федоренко) (26 April/28 April 1917 – 1 April 2006) was a Russian economist and chemist.
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Nl (format)
nl is a file format for presenting and archiving mathematical programming problems.
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Nonlinear programming
In mathematics, nonlinear programming is the process of solving an optimization problem defined by a system of equalities and inequalities, collectively termed constraints, over a set of unknown real variables, along with an objective function to be maximized or minimized, where some of the constraints or the objective function are nonlinear.
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Nullspace property
In compressed sensing, the nullspace property gives necessary and sufficient conditions on the reconstruction of sparse signals using the techniques of \ell_1-relaxation.
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Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).
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Open energy system models
Open energy system models are energy system models that are open source.
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Operations management
Operations management is an area of management concerned with designing and controlling the process of production and redesigning business operations in the production of goods or services.
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Operations research
Operations research, or operational research in British usage, is a discipline that deals with the application of advanced analytical methods to help make better decisions.
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Optimization Toolbox
Optimization Toolbox is an optimization software package developed by MathWorks.
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OptimJ
OptimJ is an extension of the Java with language support for writing optimization models and abstractions for bulk data processing.
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Oriented matroid
An oriented matroid is a mathematical structure that abstracts the properties of directed graphs and of arrangements of vectors in a vector space over an ordered field (particularly for partially ordered vector spaces).
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Outline of academic disciplines
An academic discipline or field of study is a branch of knowledge that is taught and researched as part of higher education.
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Outline of finance
The following outline is provided as an overview of and topical guide to finance: Finance – addresses the ways in which individuals and organizations raise and allocate monetary resources over time, taking into account the risks entailed in their projects.
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Outline of science
The following outline is provided as a topical overview of science: Science – the systematic effort of acquiring knowledge—through observation and experimentation coupled with logic and reasoning to find out what can be proved or not proved—and the knowledge thus acquired.
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P (complexity)
In computational complexity theory, P, also known as PTIME or DTIME(nO(1)), is a fundamental complexity class.
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P versus NP problem
The P versus NP problem is a major unsolved problem in computer science.
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P-complete
In complexity theory, a decision problem is P-complete (complete for the complexity class '''P''') if it is in P and every problem in P can be reduced to it by an appropriate reduction.
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Paris Kanellakis Award
The Paris Kanellakis Theory and Practice Award is granted yearly by the Association for Computing Machinery (ACM) to honor "specific theoretical accomplishments that have had a significant and demonstrable effect on the practice of computing".
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Paul Tseng
Paul Tseng was a Taiwanese-born American and Canadian applied mathematician and a professor at the Department of Mathematics at the University of Washington, in Seattle, Washington.
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Perfect graph
In graph theory, a perfect graph is a graph in which the chromatic number of every induced subgraph equals the size of the largest clique of that subgraph.
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Philip Wolfe (mathematician)
Philip Starr "Phil" Wolfe (August 11, 1927 – December 29, 2016) was an American mathematician and one of the founders of convex optimization theory and mathematical programming.
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Pinch analysis
Pinch analysis is a methodology for minimising energy consumption of chemical processes by calculating thermodynamically feasible energy targets (or minimum energy consumption) and achieving them by optimising heat recovery systems, energy supply methods and process operating conditions.
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Planted motif search
In the field of computational biology, a planted motif search (PMS) also known as a (l, d)-motif search (LDMS) is a method for identifying conserved motifs within a set of nucleic acid or peptide sequences.
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Policy capturing
Policy capturing or "the PC technique" is a statistical method used in social psychology to quantify the relationship between a person's judgement and the information that was used to make that judgement.
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Polyhedral combinatorics
Polyhedral combinatorics is a branch of mathematics, within combinatorics and discrete geometry, that studies the problems of counting and describing the faces of convex polyhedra and higher-dimensional convex polytopes.
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Polyhedron
In geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices.
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Polytope
In elementary geometry, a polytope is a geometric object with "flat" sides.
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Portfolio optimization
Portfolio optimization is the process of selecting the best portfolio (asset distribution), out of the set of all portfolios being considered, according to some objective.
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Power system simulation
Electrical power system simulation involves power system modeling and network simulation in order to analyze electrical power systems using design/offline or real-time data.
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Power-flow study
In power engineering, the power-flow study, or load-flow study, is a numerical analysis of the flow of electric power in an interconnected system.
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Pricing science
Pricing science is the application of social and business science methods to the problem of setting prices.
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Project production management
Project production management (PPM) is the application of operations managementA Guide to the Project Management Body of Knowledge, Fifth Edition, Project Management Institute Sec 1.5.1.1, p13 http://www.pmi.org/pmbok-guide-standards/foundational/pmbok to the delivery of capital projects.
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Protein design
Protein design is the rational design of new protein molecules to design novel activity, behavior, or purpose, and to advance basic understanding of protein function.
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Prune and search
Prune and search is a method of solving optimization problems suggested by Nimrod Megiddo in 1983.
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Pseudoconvex function
In convex analysis and the calculus of variations, branches of mathematics, a pseudoconvex function is a function that behaves like a convex function with respect to finding its local minima, but need not actually be convex.
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Pseudoforest
In graph theory, a pseudoforest is an undirected graphThe kind of undirected graph considered here is often called a multigraph or pseudograph, to distinguish it from a simple graph.
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Qoca
Qoca is a GPL library for incrementally solving systems of linear equations with various goal functions.
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Quadratic knapsack problem
The quadratic knapsack problem (QKP), first introduced in 19th century, is an extension of knapsack problem that allows for quadratic terms in the objective function: Given a set of items, each with a weight, a value, and an extra profit that can be earned if two items are selected, determine the number of item to include in a collection without exceeding capacity of the knapsack, so as to maximize the overall profit.
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Quadratic programming
Quadratic programming (QP) is the process of solving a special type of mathematical optimization problem—specifically, a (linearly constrained) quadratic optimization problem, that is, the problem of optimizing (minimizing or maximizing) a quadratic function of several variables subject to linear constraints on these variables.
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Quadratically constrained quadratic program
In mathematical optimization, a quadratically constrained quadratic program (QCQP) is an optimization problem in which both the objective function and the constraints are quadratic functions.
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Quantile regression
Quantile regression is a type of regression analysis used in statistics and econometrics.
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Radhia Cousot
Radhia Cousot (6 August 1947 – 1 May 2014) was a French computer scientist known for inventing abstract interpretation.
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Raimund Seidel
Raimund G. Seidel is a German and Austrian theoretical computer scientist and an expert in computational geometry.
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Ralph E. Gomory
Ralph Edward Gomory (born 7 May 1929) is an American applied mathematician and executive.
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RAND Corporation
RAND Corporation ("Research ANd Development") is an American nonprofit global policy think tank created in 1948 by Douglas Aircraft Company to offer research and analysis to the United States Armed Forces.
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Randomised decision rule
In statistical decision theory, a randomised decision rule or mixed decision rule is a decision rule that associates probabilities with deterministic decision rules.
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Randomized rounding
Within computer science and operations research, many combinatorial optimization problems are computationally intractable to solve exactly (to optimality).
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Rayleigh quotient
In mathematics, for a given complex Hermitian matrix M and nonzero vector x, the Rayleigh quotient R(M, x), is defined as: For real matrices and vectors, the condition of being Hermitian reduces to that of being symmetric, and the conjugate transpose x^ to the usual transpose x'.
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Reachability problem
Reachability is a fundamental problem that appears in several different contexts: finite- and infinite-state concurrent systems, computational models like cellular automata and Petri nets, program analysis, discrete and continuous systems, time critical systems, hybrid systems, rewriting systems, probabilistic and parametric systems, and open systems modelled as games.
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Reasoning system
In information technology a reasoning system is a software system that generates conclusions from available knowledge using logical techniques such as deduction and induction.
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Reduced cost
In linear programming, reduced cost, or opportunity cost, is the amount by which an objective function coefficient would have to improve (so increase for maximization problem, decrease for minimization problem) before it would be possible for a corresponding variable to assume a positive value in the optimal solution.
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Relaxation (approximation)
In mathematical optimization and related fields, relaxation is a modeling strategy.
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Relaxation (iterative method)
In numerical mathematics, relaxation methods are iterative methods for solving systems of equations, including nonlinear systems.
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Rental harmony
Rental harmony is a kind of a fair division problem in which indivisible items and a fixed monetary cost have to be divided simultaneously.
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Retiming
Retiming is the technique of moving the structural location of latches or registers in a digital circuit to improve its performance, area, and/or power characteristics in such a way that preserves its functional behavior at its outputs.
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Revenue management
Revenue management is the application of disciplined analytics that predict consumer behaviour at the micro-market level and optimize product availability and price to maximize revenue growth.
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Revised simplex method
In mathematical optimization, the revised simplex method is a variant of George Dantzig's simplex method for linear programming.
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Richard A. Tapia
Richard Alfred Tapia (born March 25, 1939) is an American mathematician and champion of under-represented minorities in the sciences.
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Richard Stockbridge
Richard H. Stockbridge is a Distinguished Professor of Mathematics at the University of Wisconsin-Milwaukee.
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Robert G. Bland
Robert Gary Bland (born February 25, 1948) is an American mathematician and operations researcher, a professor of operations research and information engineering at Cornell University.
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Robert J. Vanderbei
Robert J. Vanderbei (born 1955) is an American mathematician and Professor in the Department of Operations Research and Financial Engineering at Princeton University.
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Robert Solow
Robert Merton Solow, GCIH (born August 23, 1924), is an American economist, particularly known for his work on the theory of economic growth that culminated in the exogenous growth model named after him.
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Robust optimization
Robust optimization is a field of optimization theory that deals with optimization problems in which a certain measure of robustness is sought against uncertainty that can be represented as deterministic variability in the value of the parameters of the problem itself and/or its solution.
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Ron Shamir
Ron Shamir (Hebrew: רון שמיר; born 29 November 1953) is an Israeli professor of computer science known for his work in graph theory and in computational biology.
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Routing and wavelength assignment
The routing and wavelength assignment (RWA) problem is an optical networking problem with the goal of maximizing the number of optical connections.
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Satisfiability
In mathematical logic, satisfiability and validity are elementary concepts of semantics.
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Schedule
A schedule or a timetable, as a basic time-management tool, consists of a list of times at which possible tasks, events, or actions are intended to take place, or of a sequence of events in the chronological order in which such things are intended to take place.
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SCIP (optimization software)
SCIP (Solving Constraint Integer Programs) is a mixed integer programming solver and a framework for Branch and cut and Branch and price, developed primarily at Zuse Institute Berlin.
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SEAC (computer)
SEAC (Standards Eastern Automatic Computer or Standards Electronic Automatic Computer) was a first-generation electronic computer, built in 1950 by the U.S. National Bureau of Standards (NBS) and was initially called the National Bureau of Standards Interim Computer, because it was a small-scale computer designed to be built quickly and put into operation while the NBS waited for more powerful computers to be completed (the DYSEAC).
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Search-based software engineering
Search-based software engineering (SBSE) applies metaheuristic search techniques such as genetic algorithms, simulated annealing and tabu search to software engineering problems.
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Second-order cone programming
A second-order cone program (SOCP) is a convex optimization problem of the form where the problem parameters are f \in \mathbb^n, \ A_i \in \mathbb^, \ b_i \in \mathbb^, \ c_i \in \mathbb^n, \ d_i \in \mathbb, \ F \in \mathbb^, and g \in \mathbb^p.
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Selmer M. Johnson
Selmer Martin Johnson (21 May 1916 – 26 June 1996) was an American mathematician, a researcher at the RAND Corporation.
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Semidefinite programming
Semidefinite programming (SDP) is a subfield of convex optimization concerned with the optimization of a linear objective function (a user-specified function that the user wants to minimize or maximize) over the intersection of the cone of positive semidefinite matrices with an affine space, i.e., a spectrahedron.
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Sequential linear-quadratic programming
Sequential linear-quadratic programming (SLQP) is an iterative method for nonlinear optimization problems where objective function and constraints are twice continuously differentiable.
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Sergei Nikolaevich Chernikov
Sergei Nikolaevich Chernikov (11 May 1912 – 23 January 1987; Сергей Николаевич Черников) was a Russian mathematician who contributed significantly to the development of infinite group theory and linear inequalities.
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Set cover problem
The set cover problem is a classical question in combinatorics, computer science and complexity theory.
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Set estimation
In statistics, a random vector x is classically represented by a probability density function.
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Set packing
Set packing is a classical NP-complete problem in computational complexity theory and combinatorics, and was one of Karp's 21 NP-complete problems.
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Shadow price
A shadow price is commonly referred to as a monetary value assigned to currently unknowable or difficult-to-calculate costs.
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Shapley–Folkman lemma
The Shapley–Folkman lemma is a result in convex geometry with applications in mathematical economics that describes the Minkowski addition of sets in a vector space.
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Shortest path problem
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.
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Simon Kuznets
Simon Smith Kuznets (p; April 30, 1901 – July 8, 1985) was a Russo-American economist and statistician who received the 1971 Nobel Memorial Prize in Economic Sciences "for his empirically founded interpretation of economic growth which has led to new and deepened insight into the economic and social structure and process of development." Kuznets made a decisive contribution to the transformation of economics into an empirical science and to the formation of quantitative economic history.
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Simplex
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.
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Simplex algorithm
In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming.
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Simulation-based optimization
Simulation-based optimization integrates optimization techniques into simulation analysis.
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Slack variable
In an optimization problem, a slack variable is a variable that is added to an inequality constraint to transform it into an equality.
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Smale's problems
Smale's problems are a list of eighteen unsolved problems in mathematics that was proposed by Steve Smale in 1998, republished in 1999.
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Smallest-circle problem
The smallest-circle problem or minimum covering circle problem is a mathematical problem of computing the smallest circle that contains all of a given set of points in the Euclidean plane.
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Smart market
A smart market is a periodic auction which is cleared by the operations research technique of mathematical optimization, such as linear programming.
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Socialist calculation debate
The socialist calculation debate (sometimes known as the economic calculation debate) was a discourse on the subject of how a socialist economy would perform economic calculation given the absence of the law of value, money, financial prices for capital goods, and private ownership of the means of production.
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Software development effort estimation
Software development effort estimation is the process of predicting the most realistic amount of effort (expressed in terms of person-hours or money) required to develop or maintain software based on incomplete, uncertain and noisy input.
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Software patent
A software patent is a patent on a piece of software, such as a computer program, libraries, user interface, or algorithm.
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Soviet-type economic planning
Soviet-type economic planning (STP) is the specific model of centralized economic planning employed by Marxist-Leninist socialist states modeled on the economy of the Soviet Union.
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Sparse approximation
Sparse Approximation (also known as Sparse Representation) theory deals with sparse solutions for systems of linear equations.
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Sridhar Tayur
Sridhar R. Tayur is an American business professor, entrepreneur, and management thinker.
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Star-shaped polygon
A star-shaped polygon is a polygonal region in the plane that is a star domain, that is, a polygon that contains a point from which the entire polygon boundary is visible.
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Steven J. Miller
Steven Joel Miller is a mathematician who specializes in analytic number theory and has also worked in applied fields such as sabermetrics and linear programming.
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Stigler diet
The Stigler diet is an optimization problem named for George Stigler, a 1982 Nobel Laureate in economics, who posed the following problem: The nutrient RDAs required to be met in Stigler’s experiment were calories, protein, calcium, iron, vitamin A, thiamine, riboflavin, niacin, and ascorbic acid.
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Stochastic programming
In the field of mathematical optimization, stochastic programming is a framework for modeling optimization problems that involve uncertainty.
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Strong duality
Strong duality is a condition in mathematical optimization in which the primal optimal objective and the dual optimal objective are equal.
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Theodore Motzkin
Theodore Samuel Motzkin (26 March 1908 – 15 December 1970) was an Israeli-American mathematician.
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Theory of constraints
The theory of constraints (TOC) is a management paradigm that views any manageable system as being limited in achieving more of its goals by a very small number of constraints.
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Theory of two-level planning
The theory of two-level planning (alternatively, Kornai–Liptak decomposition) is a method that decomposes large problems of linear optimization into sub-problems.
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Thomas L. Saaty
Thomas L. Saaty (July 18, 1926 – August 14, 2017) was a Distinguished University Professor at the University of Pittsburgh, where he taught in the Joseph M. Katz Graduate School of Business.
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Time complexity
In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.
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Tixati
Tixati is a proprietary Linux and Windows BitTorrent client written in C++ designed to be light on system resources.
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Tobias Dantzig
Tobias Dantzig (February 19, 1884 – August 9, 1956) was a mathematician of Baltic German and Russian American heritage, the father of George Dantzig, and the author of Number: The Language of Science (A critical survey written for the cultured non-mathematician) (1930) and Aspects of Science (New York, Macmillan, 1937).
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TOMLAB
The TOMLAB Optimization Environment is a modeling platform for solving applied optimization problems in MATLAB.
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TOMNET
The TOMNET optimization Environment is a platform for solving applied optimization problems in Microsoft.NET.
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TomSym
The TomSym MATLAB symbolic modeling engine is a platform for modeling applied optimization and optimal control problems.
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Total dual integrality
In mathematical optimization, total dual integrality is a sufficient condition for the integrality of a polyhedron.
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Trajectory optimization
Trajectory optimization is the process of designing a trajectory that minimizes (or maximizes) some measure of performance while satisfying a set of constraints.
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Transportation theory (mathematics)
In mathematics and economics, transportation theory or transport theory is a name given to the study of optimal transportation and allocation of resources.
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Travelling salesman problem
The travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in operations research and theoretical computer science.
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Unimodular matrix
In mathematics, a unimodular matrix M is a square integer matrix having determinant +1 or −1.
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Unique sink orientation
In mathematics, a unique sink orientation is an orientation of the edges of a polytope such that, in every face of the polytope (including the whole polytope as one of the faces), there is exactly one vertex for which all adjoining edges are oriented inward (i.e. towards that vertex).
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Utility maximization problem
In microeconomics, the utility maximization problem is the problem consumers face: "how should I spend my money in order to maximize my utility?" It is a type of optimal decision problem.
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Variable neighborhood search
Variable neighborhood search (VNS), proposed by Mladenović, Hansen, 1997, is a metaheuristic method for solving a set of combinatorial optimization and global optimization problems.
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Václav Chvátal
Václav (Vašek) Chvátal (is a Professor Emeritus in the Department of Computer Science and Software Engineering at Concordia University in Montreal, Canada. He has published extensively on topics in graph theory, combinatorics, and combinatorial optimization.
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Vertex cover
In the mathematical discipline of graph theory, a vertex cover (sometimes node cover) of a graph is a set of vertices such that each edge of the graph is incident to at least one vertex of the set.
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Victor Klee
Victor L. Klee, Jr. (September 18, 1925, San Francisco – August 17, 2007, Lakewood, Ohio) was a mathematician specialising in convex sets, functional analysis, analysis of algorithms, optimization, and combinatorics.
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Victor Zalgaller
Victor (Viktor) Abramovich Zalgaller (ויקטור אבּרמוביץ' זלגלר; Виктор Абрамович Залгаллер; born on December 25, 1920 in Parfino, Novgorod Governorate) is a mathematician in the fields of geometry and optimization.
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Wald's maximin model
In decision theory and game theory, Wald's maximin model is a non-probabilistic decision-making model according to which decisions are ranked on the basis of their worst-case outcomes – the optimal decision is one with the least worst outcome.
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Weak duality
In applied mathematics, weak duality is a concept in optimization which states that the duality gap is always greater than or equal to 0.
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Weak ordering
In mathematics, especially order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set, some of whose members may be tied with each other.
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William W. Cooper
William Wager Cooper (July 23, 1914 – June 20, 2012) was an American operations researcher, known as a father of management science and as "Mr.
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Workflow
A workflow consists of an orchestrated and repeatable pattern of business activity enabled by the systematic organization of resources into processes that transform materials, provide services, or process information.
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Workforce modeling
Workforce modeling is the process by which the need for skilled workers at a particular point in time (demand) is matched directly with the availability and preference of skilled workers (supply).
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Yield curve
In finance, the yield curve is a curve showing several yields or interest rates across different contract lengths (2 month, 2 year, 20 year, etc....) for a similar debt contract.
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Yinyu Ye
Yinyu Ye (born 1948) is a Chinese American theoretical computer scientist working on mathematical optimization.
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Zadeh's Rule
In mathematical optimization, Zadeh's rule (also known as Least-entered rule) is an algorithmic refinement of the simplex method for linear optimization.
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Zero-sum game
In game theory and economic theory, a zero-sum game is a mathematical representation of a situation in which each participant's gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants.
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Zionts–Wallenius method
The Zionts–Wallenius method is an interactive method used to find a best solution to a multi-criteria optimization problem.
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1947 in science
The year 1947 in science and technology involved some significant events, listed below.
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1965 Soviet economic reform
The 1965 Soviet economic reform, sometimes called the Kosygin reform or Liberman reform, were a set of planned changes in the economy of the Soviet Union (USSR).
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References
[1] https://en.wikipedia.org/wiki/Linear_programming
