Table of Contents
185 relations: Abundance of the chemical elements, Affine transformation, AIMMS, Albert W. Tucker, Algebraic modeling language, ALGLIB, Algorithm, AMPL, Analytica (software), Apache License, API, APMonitor, Approximation algorithm, Artelys Knitro, Assignment problem, Automated planning and scheduling, Benders decomposition, Big O notation, Block diagram, Block matrix, Branch and bound, Branch and cut, Branch and price, BSD licenses, Canonical form, Cassowary (software), COIN-OR, Column generation, Combinatorial optimization, Concave function, Constraint (mathematics), Convex cone, Convex function, Convex optimization, Convex polytope, Copyleft, Covering problems, CPLEX, Criss-cross algorithm, Cutting-plane method, Dantzig–Wolfe decomposition, David S. Johnson, Distance (graph theory), Dominating set, Dual linear program, Duality (optimization), Dynamic programming, Dynamical system, Economics, Ellipsoid method, ... Expand index (135 more) »
- Convex optimization
- P-complete problems
Abundance of the chemical elements
The abundance of the chemical elements is a measure of the occurrence of the chemical elements relative to all other elements in a given environment.
See Linear programming and Abundance of the chemical elements
Affine transformation
In Euclidean geometry, an affine transformation or affinity (from the Latin, affinis, "connected with") is a geometric transformation that preserves lines and parallelism, but not necessarily Euclidean distances and angles.
See Linear programming and Affine transformation
AIMMS
AIMMS (acronym for Advanced Interactive Multidimensional Modeling System) is a prescriptive analytics software company with offices in the Netherlands, United States and Singapore.
See Linear programming and AIMMS
Albert W. Tucker
Albert William Tucker (28 November 1905 – 25 January 1995) was a Canadian mathematician who made important contributions in topology, game theory, and non-linear programming.
See Linear programming and Albert W. Tucker
Algebraic modeling language
Algebraic modeling languages (AML) are high-level computer programming languages for describing and solving high complexity problems for large scale mathematical computation (i.e. large scale optimization type problems).
See Linear programming and Algebraic modeling language
ALGLIB
ALGLIB is a cross-platform open source numerical analysis and data processing library.
See Linear programming and ALGLIB
Algorithm
In mathematics and computer science, an algorithm is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation.
See Linear programming and Algorithm
AMPL
AMPL (A Mathematical Programming Language) is an algebraic modeling language to describe and solve high-complexity problems for large-scale mathematical computing (e.g. large-scale optimization and scheduling-type problems).
See Linear programming and AMPL
Analytica (software)
Analytica is a visual software developed by Lumina Decision Systems for creating, analyzing and communicating quantitative decision models.
See Linear programming and Analytica (software)
Apache License
The Apache License is a permissive free software license written by the Apache Software Foundation (ASF).
See Linear programming and Apache License
API
An is a way for two or more computer programs or components to communicate with each other.
See Linear programming and API
APMonitor
Advanced process monitor (APMonitor) is a modeling language for differential algebraic (DAE) equations.
See Linear programming and APMonitor
Approximation algorithm
In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to optimization problems (in particular NP-hard problems) with provable guarantees on the distance of the returned solution to the optimal one.
See Linear programming and Approximation algorithm
Artelys Knitro
Artelys Knitro is a commercial software package for solving large scale nonlinear mathematical optimization problems.
See Linear programming and Artelys Knitro
Assignment problem
The assignment problem is a fundamental combinatorial optimization problem.
See Linear programming and Assignment problem
Automated planning and scheduling
Automated planning and scheduling, sometimes denoted as simply AI planning, is a branch of artificial intelligence that concerns the realization of strategies or action sequences, typically for execution by intelligent agents, autonomous robots and unmanned vehicles.
See Linear programming and Automated planning and scheduling
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.
See Linear programming and Benders decomposition
Big O notation
Big O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity.
See Linear programming and Big O notation
Block diagram
A block diagram is a diagram of a system in which the principal parts or functions are represented by blocks connected by lines that show the relationships of the blocks.
See Linear programming and Block diagram
Block matrix
In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices.
See Linear programming and Block matrix
Branch and bound
Branch and bound (BB, B&B, or BnB) is a method for solving optimization problems by breaking them down into smaller sub-problems and using a bounding function to eliminate sub-problems that cannot contain the optimal solution.
See Linear programming and Branch and bound
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.
See Linear programming and Branch and cut
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.
See Linear programming and Branch and price
BSD licenses
BSD licenses are a family of permissive free software licenses, imposing minimal restrictions on the use and distribution of covered software.
See Linear programming and BSD licenses
Canonical form
In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression.
See Linear programming and Canonical form
Cassowary (software)
Cassowary is an incremental constraint solving toolkit that efficiently solves systems of linear equalities and inequalities.
See Linear programming and Cassowary (software)
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.
See Linear programming and COIN-OR
Column generation
Column generation or delayed column generation is an efficient algorithm for solving large linear programs.
See Linear programming and Column generation
Combinatorial optimization
Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the set of feasible solutions is discrete or can be reduced to a discrete set.
See Linear programming and Combinatorial optimization
Concave function
In mathematics, a concave function is one for which the value at any convex combination of elements in the domain is greater than or equal to the convex combination of the values at the endpoints.
See Linear programming and Concave function
Constraint (mathematics)
In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy.
See Linear programming and Constraint (mathematics)
Convex cone
In linear algebra, a cone—sometimes called a linear cone for distinguishing it from other sorts of cones—is a subset of a vector space that is closed under positive scalar multiplication; that is, is a cone if x\in C implies sx\in C for every.
See Linear programming and Convex cone
Convex function
In mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above the graph between the two points.
See Linear programming and Convex function
Convex optimization
Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets).
See Linear programming and Convex optimization
Convex polytope
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the n-dimensional Euclidean space \mathbb^n.
See Linear programming and Convex polytope
Copyleft
Copyleft is the legal technique of granting certain freedoms over copies of copyrighted works with the requirement that the same rights be preserved in derivative works.
See Linear programming and Copyleft
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.
See Linear programming and Covering problems
CPLEX
IBM ILOG CPLEX Optimization Studio (often informally referred to simply as CPLEX) is an optimization software package.
See Linear programming and CPLEX
Criss-cross algorithm
In mathematical optimization, the criss-cross algorithm is any of a family of algorithms for linear programming. Linear programming and criss-cross algorithm are geometric algorithms.
See Linear programming and Criss-cross algorithm
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.
See Linear programming and Cutting-plane method
Dantzig–Wolfe decomposition
Dantzig–Wolfe decomposition is an algorithm for solving linear programming problems with special structure.
See Linear programming and Dantzig–Wolfe decomposition
David S. Johnson
David Stifler Johnson (December 9, 1945 – March 8, 2016) was an American computer scientist specializing in algorithms and optimization.
See Linear programming and David S. Johnson
Distance (graph theory)
In the mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path (also called a graph geodesic) connecting them.
See Linear programming and Distance (graph theory)
Dominating set
In graph theory, a dominating set for a graph is a subset of its vertices, such that any vertex of is in, or has a neighbor in.
See Linear programming and Dominating set
Dual linear program
The dual of a given linear program (LP) is another LP that is derived from the original (the primal) LP in the following schematic way.
See Linear programming and Dual linear program
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. Linear programming and duality (optimization) are convex optimization.
See Linear programming and Duality (optimization)
Dynamic programming
Dynamic programming is both a mathematical optimization method and an algorithmic paradigm.
See Linear programming and Dynamic programming
Dynamical system
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve.
See Linear programming and Dynamical system
Economics
Economics is a social science that studies the production, distribution, and consumption of goods and services.
See Linear programming and Economics
Ellipsoid method
In mathematical optimization, the ellipsoid method is an iterative method for minimizing convex functions over convex sets. Linear programming and ellipsoid method are convex optimization.
See Linear programming and Ellipsoid method
Feasible region
In mathematical optimization and computer science, a feasible region, feasible set, 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.
See Linear programming and Feasible region
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.
See Linear programming and FICO Xpress
Flow network
In graph theory, a flow network (also known as a transportation network) is a directed graph where each edge has a capacity and each edge receives a flow.
See Linear programming and Flow network
FortMP
FortMP is a software package for solving large-scale optimization problems.
See Linear programming and FortMP
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.
See Linear programming and Fourier–Motzkin elimination
Fractional coloring
Fractional coloring is a topic in a young branch of graph theory known as fractional graph theory.
See Linear programming and Fractional coloring
Frank Lauren Hitchcock
Frank Lauren Hitchcock (March 6, 1875 – May 31, 1957) was an American mathematician and physicist known for his formulation of the transportation problem in 1941.
See Linear programming and Frank Lauren Hitchcock
Game theory
Game theory is the study of mathematical models of strategic interactions.
See Linear programming and Game theory
Günter M. Ziegler
Günter Matthias Ziegler (born 19 May 1963) is a German mathematician who has been serving as president of the Free University of Berlin since 2018.
See Linear programming and Günter M. Ziegler
Gekko (optimization software)
The GEKKO Python package solves large-scale mixed-integer and differential algebraic equations with nonlinear programming solvers (IPOPT, APOPT, BPOPT, SNOPT, MINOS).
See Linear programming and Gekko (optimization software)
General algebraic modeling system
The general algebraic modeling system (GAMS) is a high-level modeling system for mathematical optimization.
See Linear programming and General algebraic modeling system
George Dantzig
George Bernard Dantzig (November 8, 1914 – May 13, 2005) was an American mathematical scientist who made contributions to industrial engineering, operations research, computer science, economics, and statistics.
See Linear programming and George Dantzig
GLOP
GLOP (the Google Linear Optimization Package) is Google's open source linear programming solver, created by Google's.
See Linear programming and GLOP
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.
See Linear programming and GNU Linear Programming Kit
Graph (discrete mathematics)
In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some sense "related".
See Linear programming and Graph (discrete mathematics)
Gurobi Optimizer
Gurobi Optimizer is a prescriptive analytics platform and a decision-making technology developed by Gurobi Optimization, LLC.
See Linear programming and Gurobi Optimizer
Half-space (geometry)
In geometry, a half-space is either of the two parts into which a plane divides the three-dimensional Euclidean space.
See Linear programming and Half-space (geometry)
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.
See Linear programming and Hirsch conjecture
IMSL Numerical Libraries
IMSL (International Mathematics and Statistics Library) is a commercial collection of software libraries of numerical analysis functionality that are implemented in the computer programming languages C, Java, C#.NET, and Fortran.
See Linear programming and IMSL Numerical Libraries
Independent set (graph theory)
In graph theory, an independent set, stable set, coclique or anticlique is a set of vertices in a graph, no two of which are adjacent.
See Linear programming and Independent set (graph theory)
Input–output model
In economics, an input–output model is a quantitative economic model that represents the interdependencies between different sectors of a national economy or different regional economies.
See Linear programming and Input–output model
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.
See Linear programming and Integer programming
Interior-point method
Interior-point methods (also referred to as barrier methods or IPMs) are algorithms for solving linear and non-linear convex optimization problems.
See Linear programming and Interior-point method
Intersection
In mathematics, the intersection of two or more objects is another object consisting of everything that is contained in all of the objects simultaneously.
See Linear programming and Intersection
Iterative method
In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones.
See Linear programming and Iterative method
Job-shop scheduling
Job-shop scheduling, the job-shop problem (JSP) or job-shop scheduling problem (JSSP) is an optimization problem in computer science and operations research.
See Linear programming and Job-shop scheduling
John von Neumann
John von Neumann (Neumann János Lajos; December 28, 1903 – February 8, 1957) was a Hungarian and American mathematician, physicist, computer scientist, engineer and polymath.
See Linear programming and John von Neumann
Joseph Fourier
Jean-Baptiste Joseph Fourier (21 March 1768 – 16 May 1830) was a French mathematician and physicist born in Auxerre and best known for initiating the investigation of Fourier series, which eventually developed into Fourier analysis and harmonic analysis, and their applications to problems of heat transfer and vibrations.
See Linear programming and Joseph Fourier
JuMP
JuMP is an algebraic modeling language and a collection of supporting packages for mathematical optimization embedded in the Julia programming language.
See Linear programming and JuMP
Karmarkar's algorithm
Karmarkar's algorithm is an algorithm introduced by Narendra Karmarkar in 1984 for solving linear programming problems.
See Linear programming and Karmarkar's algorithm
Karp's 21 NP-complete problems
In computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete.
See Linear programming and Karp's 21 NP-complete problems
Klee–Minty cube
The Klee–Minty cube or Klee–Minty polytope (named after Victor Klee and George J. Minty) is a unit hypercube of variable dimension whose corners have been perturbed.
See Linear programming and Klee–Minty cube
Least absolute deviations
Least absolute deviations (LAD), also known as least absolute errors (LAE), least absolute residuals (LAR), or least absolute values (LAV), is a statistical optimality criterion and a statistical optimization technique based on minimizing the sum of absolute deviations (also sum of absolute residuals or sum of absolute errors) or the ''L''1 norm of such values.
See Linear programming and Least absolute deviations
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.
See Linear programming and Least-squares spectral analysis
Leonid Khachiyan
Leonid Genrikhovich Khachiyan (Леони́д Ге́нрихович Хачия́н; May 3, 1952April 29, 2005) was a Soviet and American mathematician and computer scientist.
See Linear programming and Leonid Khachiyan
LINDO
LINDO (Linear, Interactive, and Discrete Optimizer) is a software package for linear programming, integer programming, nonlinear programming, stochastic programming and global optimization.
See Linear programming and LINDO
Linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices.
See Linear programming and Linear algebra
Linear equation
In mathematics, a linear equation is an equation that may be put in the form a_1x_1+\ldots+a_nx_n+b.
See Linear programming and Linear equation
Linear form
In mathematics, a linear form (also known as a linear functional, a one-form, or a covector) is a linear mapIn some texts the roles are reversed and vectors are defined as linear maps from covectors to scalars from a vector space to its field of scalars (often, the real numbers or the complex numbers).
See Linear programming and Linear form
Linear inequality
In mathematics a linear inequality is an inequality which involves a linear function.
See Linear programming and Linear inequality
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.
See Linear programming and Linear production game
Linear programming
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear relationships. Linear programming and linear programming are convex optimization, geometric algorithms and p-complete problems.
See Linear programming and Linear programming
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.
See Linear programming and Linear programming relaxation
Linear-fractional programming
In mathematical optimization, linear-fractional programming (LFP) is a generalization of linear programming (LP).
See Linear programming and Linear-fractional programming
Linearity
In mathematics, the term linear is used in two distinct senses for two different properties.
See Linear programming and Linearity
Lingo (programming language)
Lingo is a verbose object-oriented (OO) scripting language developed by John H. Thompson for use in Adobe Director (formerly Macromedia Director).
See Linear programming and Lingo (programming language)
Loss function
In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event.
See Linear programming and Loss function
Lp solve
lp_solve is a free software command line utility and library for solving linear programming and mixed integer programming problems.
See Linear programming and Lp solve
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.
See Linear programming and LP-type problem
Manfred W. Padberg
Manfred Wilhelm Padberg (October 10, 1941 in Bottrop, Germany–May 12, 2014) was a German mathematician who worked with linear and combinatorial optimization.
See Linear programming and Manfred W. Padberg
Maple (software)
Maple is a symbolic and numeric computing environment as well as a multi-paradigm programming language.
See Linear programming and Maple (software)
Matching (graph theory)
In the mathematical discipline of graph theory, a matching or independent edge set in an undirected graph is a set of edges without common vertices.
See Linear programming and Matching (graph theory)
Mathcad
Mathcad is computer software for the verification, validation, documentation and re-use of mathematical calculations in engineering and science, notably mechanical, chemical, electrical, and civil engineering.
See Linear programming and Mathcad
Mathematical model
A mathematical model is an abstract description of a concrete system using mathematical concepts and language.
See Linear programming and Mathematical model
Mathematical optimization
Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives.
See Linear programming and Mathematical optimization
MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.
See Linear programming and MATLAB
Matrix (mathematics)
In mathematics, a matrix (matrices) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object.
See Linear programming and Matrix (mathematics)
Matrix multiplication
In mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices.
See Linear programming and Matrix multiplication
Maximum and minimum
In mathematical analysis, the maximum and minimum of a function are, respectively, the largest and smallest value taken by the function.
See Linear programming and Maximum and minimum
Maximum principle
In the mathematical fields of differential equations and geometric analysis, the maximum principle is one of the most useful and best known tools of study.
See Linear programming and Maximum principle
Michael Garey
Michael Randolph Garey (born November 19, 1945) is a computer science researcher, and co-author (with David S. Johnson) of Computers and Intractability: A Guide to the Theory of NP-completeness.
See Linear programming and Michael Garey
Microeconomics
Microeconomics is a branch of economics that studies the behavior of individuals and firms in making decisions regarding the allocation of scarce resources and the interactions among these individuals and firms.
See Linear programming and Microeconomics
Microsoft Excel
Microsoft Excel is a spreadsheet editor developed by Microsoft for Windows, macOS, Android, iOS and iPadOS.
See Linear programming and Microsoft Excel
Minkowski addition
In geometry, the Minkowski sum of two sets of position vectors A and B in Euclidean space is formed by adding each vector in A to each vector in B: The Minkowski difference (also Minkowski subtraction, Minkowski decomposition, or geometric difference) is the corresponding inverse, where (A - B) produces a set that could be summed with B to recover A. Linear programming and Minkowski addition are geometric algorithms.
See Linear programming and Minkowski addition
MINTO
MINTO (Mixed Integer Optimizer) is an integer programming solver which uses branch and bound algorithm.
See Linear programming and MINTO
MIT License
The MIT License is a permissive software license originating at the Massachusetts Institute of Technology (MIT) in the late 1980s.
See Linear programming and MIT License
MOSEK
MOSEK is a software package for the solution of linear, mixed-integer linear, quadratic, mixed-integer quadratic, quadratically constrained, conic and convex nonlinear mathematical optimization problems.
See Linear programming and MOSEK
Mozilla Public License
The Mozilla Public License (MPL) is a free and open-source weak copyleft license for most Mozilla Foundation software such as Firefox and Thunderbird.
See Linear programming and Mozilla Public License
MPS (format)
MPS (Mathematical Programming System) is a file format for presenting and archiving linear programming (LP) and mixed integer programming problems.
See Linear programming and MPS (format)
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.
See Linear programming and Multi-commodity flow problem
NAG Numerical Library
The NAG Numerical Library is a software product developed and sold by The Numerical Algorithms Group Ltd.
See Linear programming and NAG Numerical Library
Narendra Karmarkar
Narendra Krishna Karmarkar (born circa 1956) is an Indian mathematician.
See Linear programming and Narendra Karmarkar
Naum Z. Shor
Naum Zuselevich Shor (Наум Зуселевич Шор) (1 January 1937 – 26 February 2006) was a Soviet and Ukrainian mathematician specializing in optimization.
See Linear programming and Naum Z. Shor
Network flow problem
In combinatorial optimization, network flow problems are a class of computational problems in which the input is a flow network (a graph with numerical capacities on its edges), and the goal is to construct a flow, numerical values on each edge that respect the capacity constraints and that have incoming flow equal to outgoing flow at all vertices except for certain designated terminals.
See Linear programming and Network flow problem
Nobel Memorial Prize in Economic Sciences
The Nobel Memorial Prize in Economic Sciences, officially the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel (Sveriges riksbanks pris i ekonomisk vetenskap till Alfred Nobels minne), is an economics award funded by Sveriges Riksbank and administered by the Nobel Foundation.
See Linear programming and Nobel Memorial Prize in Economic Sciences
Nonlinear programming
In mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints are not linear equalities or the objective function is not a linear function.
See Linear programming and Nonlinear programming
NP-hardness
In computational complexity theory, a computational problem H is called NP-hard if, for every problem L which can be solved in non-deterministic polynomial-time, there is a polynomial-time reduction from L to H. That is, assuming a solution for H takes 1 unit time, Hs solution can be used to solve L in polynomial time.
See Linear programming and NP-hardness
Observable universe
The observable universe is a ball-shaped region of the universe consisting of all matter that can be observed from Earth or its space-based telescopes and exploratory probes at the present time; the electromagnetic radiation from these objects has had time to reach the Solar System and Earth since the beginning of the cosmological expansion.
See Linear programming and Observable universe
Odds algorithm
In decision theory, the odds algorithm (or Bruss algorithm) is a mathematical method for computing optimal strategies for a class of problems that belong to the domain of optimal stopping problems.
See Linear programming and Odds algorithm
Odysseus
In Greek and Roman mythology, Odysseus (Odyseús), also known by the Latin variant Ulysses (Ulixes), is a legendary Greek king of Ithaca and the hero of Homer's epic poem the Odyssey.
See Linear programming and Odysseus
Operations research
Operations research (operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve decision-making.
See Linear programming and Operations research
Optimization Toolbox
Optimization Toolbox is an optimization software package developed by MathWorks.
See Linear programming and Optimization Toolbox
OptimJ
OptimJ is an extension for Java with language support for writing optimization models and abstractions for bulk data processing.
See Linear programming and OptimJ
Oriented matroid
An oriented matroid is a mathematical structure that abstracts the properties of directed graphs, vector arrangements over ordered fields, and hyperplane arrangements over ordered fields.
See Linear programming and Oriented matroid
P (complexity)
In computational complexity theory, P, also known as PTIME or DTIME(nO(1)), is a fundamental complexity class.
See Linear programming and P (complexity)
Packing problems
Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects together into containers.
See Linear programming and Packing problems
Permissive software license
A permissive software license, sometimes also called BSD-like or BSD-style license, is a free-software license which instead of copyleft protections, carries only minimal restrictions on how the software can be used, modified, and redistributed, usually including a warranty disclaimer.
See Linear programming and Permissive software license
Polytope
In elementary geometry, a polytope is a geometric object with flat sides (faces).
See Linear programming and Polytope
Proceedings of the USSR Academy of Sciences
The Proceedings of the USSR Academy of Sciences (Доклады Академии Наук СССР, Doklady Akademii Nauk SSSR (DAN SSSR), Comptes Rendus de l'Académie des Sciences de l'URSS) was a Soviet journal that was dedicated to publishing original, academic research papers in physics, mathematics, chemistry, geology, and biology.
See Linear programming and Proceedings of the USSR Academy of Sciences
Profit maximization
In economics, profit maximization is the short run or long run process by which a firm may determine the price, input and output levels that will lead to the highest possible total profit (or just profit in short).
See Linear programming and Profit maximization
Proprietary software
Proprietary software is software that grants its creator, publisher, or other rightsholder or rightsholder partner a legal monopoly by modern copyright and intellectual property law to exclude the recipient from freely sharing the software or modifying it, and—in some cases, as is the case with some patent-encumbered and EULA-bound software—from making use of the software on their own, thereby restricting their freedoms.
See Linear programming and Proprietary software
Pyomo
Pyomo is a collection of Python software packages for formulating optimization models.
See Linear programming and Pyomo
Qoca
Qoca is a GPL library for incrementally solving systems of linear equations with various goal functions.
See Linear programming and Qoca
Quadratic programming
Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions.
See Linear programming and Quadratic programming
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.
See Linear programming and Quadratically constrained quadratic program
R (programming language)
R is a programming language for statistical computing and data visualization.
See Linear programming and R (programming language)
Real number
In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.
See Linear programming and Real number
Routing
Routing is the process of selecting a path for traffic in a network or between or across multiple networks.
See Linear programming and Routing
SAS (software)
SAS (previously "Statistical Analysis System") is a statistical software suite developed by SAS Institute for data management, advanced analytics, multivariate analysis, business intelligence, criminal investigation, and predictive analytics.
See Linear programming and SAS (software)
Scheduling (production processes)
Scheduling is the process of arranging, controlling and optimizing work and workloads in a production process or manufacturing process.
See Linear programming and Scheduling (production processes)
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. Linear programming and second-order cone programming are convex optimization.
See Linear programming and Second-order cone programming
Semidefinite programming
Semidefinite programming (SDP) is a subfield of mathematical programming 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. Linear programming and semidefinite programming are convex optimization and p-complete problems.
See Linear programming and Semidefinite programming
Sequential quadratic programming
Sequential quadratic programming (SQP) is an iterative method for constrained nonlinear optimization which may be considered a quasi-Newton method.
See Linear programming and Sequential quadratic programming
Set cover problem
The set cover problem is a classical question in combinatorics, computer science, operations research, and complexity theory.
See Linear programming and Set cover problem
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.
See Linear programming and Set packing
Shadow price
A shadow price is the monetary value assigned to an abstract or intangible commodity which is not traded in the marketplace.
See Linear programming and Shadow price
Simplex algorithm
In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming.
See Linear programming and Simplex algorithm
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 constraint.
See Linear programming and Slack variable
Smale's problems
Smale's problems are a list of eighteen unsolved problems in mathematics proposed by Steve Smale in 1998 and republished in 1999.
See Linear programming and Smale's problems
Soviet Union
The Union of Soviet Socialist Republics (USSR), commonly known as the Soviet Union, was a transcontinental country that spanned much of Eurasia from 1922 to 1991.
See Linear programming and Soviet Union
Springer Science+Business Media
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
See Linear programming and Springer Science+Business Media
Stephen Smale
Stephen Smale (born July 15, 1930) is an American mathematician, known for his research in topology, dynamical systems and mathematical economics.
See Linear programming and Stephen Smale
Stochastic programming
In the field of mathematical optimization, stochastic programming is a framework for modeling optimization problems that involve uncertainty.
See Linear programming and Stochastic programming
Strong duality
Strong duality is a condition in mathematical optimization in which the primal optimal objective and the dual optimal objective are equal. Linear programming and Strong duality are convex optimization.
See Linear programming and Strong duality
Strongly-polynomial time
In computer science, a polynomial-time algorithm is generally speaking an algorithm whose running time is upper-bounded by some polynomial function of the input size.
See Linear programming and Strongly-polynomial time
SuanShu numerical library
SuanShu is a Java math library.
See Linear programming and SuanShu numerical library
Submodular flow
In the theory of combinatorial optimization, submodular flow is a general class of optimization problems that includes as special cases the minimum-cost flow problem, matroid intersection, and the problem of computing a minimum-weight dijoin in a weighted directed graph.
See Linear programming and Submodular flow
The Mathematical Intelligencer
The Mathematical Intelligencer is a mathematical journal published by Springer Science+Business Media that aims at a conversational and scholarly tone, rather than the technical and specialist tone more common among academic journals.
See Linear programming and The Mathematical Intelligencer
Time complexity
In theoretical computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm.
See Linear programming and Time complexity
Tjalling Koopmans
Tjalling Charles Koopmans (August 28, 1910 – February 26, 1985) was a Dutch-American mathematician and economist.
See Linear programming and Tjalling Koopmans
TOMLAB
The TOMLAB Optimization Environment is a modeling platform for solving applied optimization problems in MATLAB.
See Linear programming and TOMLAB
Total dual integrality
In mathematical optimization, total dual integrality is a sufficient condition for the integrality of a polyhedron.
See Linear programming and Total dual integrality
Travelling salesman problem
The travelling salesman problem, also known as the travelling salesperson 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 exactly once and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research.
See Linear programming and Travelling salesman problem
Unimodular matrix
In mathematics, a unimodular matrix M is a square integer matrix having determinant +1 or −1.
See Linear programming and Unimodular matrix
Unit cube
A unit cube, more formally a cube of side 1, is a cube whose sides are 1 unit long.
See Linear programming and Unit cube
Variable (computer science)
In computer programming, a variable is an abstract storage location paired with an associated symbolic name, which contains some known or unknown quantity of data or object referred to as a value; or in simpler terms, a variable is a named container for a particular set of bits or type of data (like integer, float, string, etc...).
See Linear programming and Variable (computer science)
Vector space
In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called ''vectors'', can be added together and multiplied ("scaled") by numbers called ''scalars''.
See Linear programming and Vector space
Vertex cover
In graph theory, a vertex cover (sometimes node cover) of a graph is a set of vertices that includes at least one endpoint of every edge of the graph.
See Linear programming and Vertex cover
VisSim
VisSim is a visual block diagram program for the simulation of dynamical systems and model-based design of embedded systems, with its own visual language.
See Linear programming and VisSim
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. Linear programming and weak duality are convex optimization.
See Linear programming and Weak duality
Wolfram Mathematica
Wolfram Mathematica is a software system with built-in libraries for several areas of technical computing that allow machine learning, statistics, symbolic computation, data manipulation, network analysis, time series analysis, NLP, optimization, plotting functions and various types of data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other programming languages.
See Linear programming and Wolfram Mathematica
Worst-case complexity
In computer science (specifically computational complexity theory), the worst-case complexity measures the resources (e.g. running time, memory) that an algorithm requires given an input of arbitrary size (commonly denoted as in asymptotic notation).
See Linear programming and Worst-case complexity
XPRESS
XPRESS was launched in the UAE on 15 March 2007 as a free weekly newspaper and competitor to the likes of 7DAYS and Emirates Today.
See Linear programming and XPRESS
Yinyu Ye
Yinyu Ye (born 1948) is a Chinese American theoretical computer scientist working on mathematical optimization.
See Linear programming and Yinyu Ye
Zuse Institute Berlin
The Zuse Institute Berlin (abbreviated ZIB, or Konrad-Zuse-Zentrum für Informationstechnik Berlin) is a research institute for applied mathematics and computer science on the campus of Freie Universität Berlin in Dahlem, Berlin, Germany.
See Linear programming and Zuse Institute Berlin
See also
Convex optimization
- Algorithmic problems on convex sets
- Barrier function
- Biconvex optimization
- Bregman method
- Center-of-gravity method
- Clarke generalized derivative
- Conic optimization
- Convex optimization
- Convexity in economics
- Danskin's theorem
- Duality (optimization)
- Duality gap
- Ellipsoid method
- Fenchel's duality theorem
- Geodesic convexity
- Geometric programming
- Lagrangian relaxation
- Linear matrix inequality
- Linear programming
- Maximum theorem
- Non-convexity (economics)
- Perturbation function
- Power cone
- Proximal gradient methods for learning
- Pseudoconvex function
- Quasiconvex function
- Second-order cone programming
- Semidefinite programming
- Separation oracle
- Shapley–Folkman lemma
- Slater's condition
- Stochastic gradient descent
- Stochastic variance reduction
- Strong duality
- Structured sparsity regularization
- Subderivative
- Subgradient method
- Test functions for optimization
- Tracking error
- Weak duality
- Wolfe duality
P-complete problems
- Horn-satisfiability
- Linear programming
- Semidefinite programming
References
Also known as 0-1 Integer programming, 0-1 integer program, 0-1 integer programs, 0-1 linear programming, 1-0 linear programming, Algorithms for linear programming, Applications of linear programming, Binary integer program, Binary integer programming, Binary integer programs, Complementary slackness, History of linear programming, Integer linear programs, Integer programs, Integral linear program, Integral polyhedron, LP duality, LP problem, Linear optimisation, Linear optimization, Linear problem, Linear program, Linear programme, Linear programmer, Linear programmers, Linear programming Formulation, Linear programming algorithms, Linear programming problem, Linear programming solvers, Linear programs, List of linear programming solvers, List of solvers for linear programming, MILP, Mixed integer linear programming, Mixed integer program, Mixed integer programming, Mixed integer programs.