179 relations: Abundance of the chemical elements, Affine transformation, AIMMS, Albert W. Tucker, Algebraic modeling language, Algorithm, AMPL, Apache License, APMonitor, Application programming interface, Approximation algorithm, Assignment problem, Automated planning and scheduling, Barrier function, Benders decomposition, Block diagram, Block matrix, Branch and bound, Branch and cut, Branch and price, BSD licenses, C++, Canonical form, Cassowary (software), Christos Papadimitriou, Coefficient, COIN-OR, Column generation, Combinatorial optimization, Comparability, Computers and Intractability, Concave function, Constraint (mathematics), Convex cone, Convex function, Convex lattice polytope, Convex optimization, Convex polytope, Convex set, Copyleft, Covering problems, CPLEX, Criss-cross algorithm, Cutting-plane method, Dantzig–Wolfe decomposition, David S. Johnson, Distance (graph theory), Dominating set, Duality (optimization), Dynamic programming, ..., Dynamical system, Economics, Economist, Ellipsoid method, Feasible region, FICO Xpress, Flow network, FortMP, Fourier–Motzkin elimination, Fractional coloring, Frank Lauren Hitchcock, Game theory, Günter M. Ziegler, General Algebraic Modeling System, George Dantzig, GNU Linear Programming Kit, GNU Multiple Precision Arithmetic Library, Gradient descent, Graph (discrete mathematics), Gurobi, Half-space (geometry), Hirsch conjecture, IMSL Numerical Libraries, Independent set (graph theory), Integer programming, Interior-point method, Intersection, Iterative method, Java (programming language), Jiří Matoušek (mathematician), Job shop scheduling, John von Neumann, Joseph Fourier, Karmarkar's algorithm, Karp's 21 NP-complete problems, Klee–Minty cube, Leonid Kantorovich, Leonid Khachiyan, LINDO, Linear equation, Linear form, Linear inequality, Linear programming relaxation, Linear-fractional programming, Linearity, Lingo (programming language), Loss function, LP-type problem, Maple (software), Mark Overmars, Matching (graph theory), Mathcad, Mathematical model, Mathematical optimization, MATLAB, Matrix (mathematics), Maxima and minima, Maximum principle, Michael Garey, Microeconomics, Microsoft Excel, Minkowski addition, MINTO, MOSEK, Multiple discovery, NAG Numerical Library, Narendra Karmarkar, Naum Z. Shor, NMath Stats, Nobel Memorial Prize in Economic Sciences, Nonlinear programming, NP-hardness, Numerical Algorithms Group, Observable universe, Odysseus, Operations research, Optimization Toolbox, OptimJ, Oriented matroid, P (complexity), Packing problems, Permissive software licence, Polyhedron, Polytope, Proceedings of the USSR Academy of Sciences, Profit maximization, Proprietary software, Pyomo, Python (programming language), Qoca, Quadratic programming, R (programming language), Real number, Routing, SAS (software), Scheduling (production processes), SCIP (optimization software), Semidefinite programming, Set cover problem, Set packing, Shadow price, Simplex algorithm, Slack variable, Smale's problems, Soviet Union, Springer Science+Business Media, Stephen Smale, Stochastic programming, Strong duality, Submodular set function, The Mathematical Intelligencer, Time complexity, Tjalling Koopmans, TOMLAB, Total dual integrality, Transpose, Travelling salesman problem, Unimodular matrix, Unit cube, Variable (computer science), Vector space, Vertex cover, VisSim, Weak duality, Wolfram Mathematica, World War II, Worst-case complexity, Yinyu Ye, .NET Framework. Expand index (129 more) »

## 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.

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## Affine transformation

In geometry, an affine transformation, affine mapBerger, Marcel (1987), p. 38.

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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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## 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.

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## 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).

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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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## 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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## Apache License

The Apache License is a permissive free software license written by the Apache Software Foundation (ASF).

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## APMonitor

Advanced process monitor (APMonitor), is a modeling language for differential algebraic (DAE) equations.

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## Application programming interface

In computer programming, an application programming interface (API) is a set of subroutine definitions, protocols, and tools for building software.

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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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## 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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## 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.

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## Barrier function

In constrained optimization, a field of mathematics, a barrier function is a continuous function whose value on a point increases to infinity as the point approaches the boundary of the feasible region of an optimization problem.

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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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## 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.

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## 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.

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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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## BSD licenses

BSD licenses are a family of permissive free software licenses, imposing minimal restrictions on the use and redistribution of covered software.

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## C++

C++ ("see plus plus") is a general-purpose programming language.

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## 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.

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## Cassowary (software)

Cassowary is an incremental constraint solving toolkit that efficiently solves systems of linear equalities and inequalities.

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## Christmas

Christmas is an annual festival commemorating the birth of Jesus Christ,Martindale, Cyril Charles.

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## Christmas and holiday season

The Christmas season, also called the festive season, or the holiday season (mainly in the U.S. and Canada; often simply called the holidays),, is an annually recurring period recognized in many Western and Western-influenced countries that is generally considered to run from late November to early January.

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## Christmas Eve

Christmas Eve is the evening or entire day before Christmas Day, the festival commemorating the birth of Jesus.

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## Christmas traditions

Christmas traditions vary from country to country.

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## Christos Papadimitriou

Christos Harilaos Papadimitriou (Greek: Χρήστος Χαρίλαος Παπαδημητρίου; born August 16, 1949) is a Greek theoretical computer scientist, and professor of Computer Science at Columbia University.

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## Coefficient

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series or any expression; it is usually a number, but may be any expression.

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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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## 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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## Comparability

In mathematics, any two elements x and y of a set P that is partially ordered by a binary relation ≤ are comparable when either x ≤ y or y ≤ x. If it is not the case that x and y are comparable, then they are called incomparable.

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## Computers and Intractability

In computer science, more specifically computational complexity theory, Computers and Intractability: A Guide to the Theory of NP-Completeness is an influential textbook by Michael Garey and David S. Johnson.

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## Concave function

In mathematics, a concave function is the negative of a convex function.

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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 cone

In linear algebra, a convex cone is a subset of a vector space over an ordered field that is closed under linear combinations with positive coefficients.

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## Convex function

In mathematics, a real-valued function defined on an ''n''-dimensional interval is called convex (or convex downward or concave upward) if the line segment between any two points on the graph of the function lies above or on the graph, in a Euclidean space (or more generally a vector space) of at least two dimensions.

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## Convex lattice polytope

A convex lattice polytope (also called Z-polyhedron or Z-polytope) is a geometric object playing an important role in discrete geometry and combinatorial commutative algebra.

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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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## Convex set

In convex geometry, a convex set is a subset of an affine space that is closed under convex combinations.

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## Copyleft

Copyleft (a play on the word copyright) is the practice of offering people the right to freely distribute copies and modified versions of a work with the stipulation that the same rights be preserved in derivative works down the line.

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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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## Criss-cross algorithm

In mathematical optimization, the criss-cross algorithm is any of a family of algorithms for linear programming.

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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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## David S. Johnson

David Stifler Johnson (December 9, 1945 – March 8, 2016) was an American computer scientist specializing in algorithms and optimization.

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## 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.

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## Dominating set

In graph theory, a dominating set for a graph G.

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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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## Dynamical system

In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space.

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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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## Economist

An economist is a practitioner in the social science discipline of economics.

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## Ellipsoid method

In mathematical optimization, the ellipsoid method is an iterative method for minimizing convex functions.

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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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## 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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## 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.

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## FortMP

FortMP is a software package for solving large-scale optimization 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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## 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.

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## Game theory

Game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers".

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## Günter M. Ziegler

Günter Matthias Ziegler (born 19 May 1963) is a German mathematician.

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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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## 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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## GNU Multiple Precision Arithmetic Library

GNU Multiple Precision Arithmetic Library (GMP) is a free library for arbitrary-precision arithmetic, operating on signed integers, rational numbers, and floating point numbers.

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## Gradient descent

Gradient descent is a first-order iterative optimization algorithm for finding the minimum of a function.

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## Graph (discrete mathematics)

In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".

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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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## Half-space (geometry)

In geometry, a half-space is either of the two parts into which a plane divides the three-dimensional Euclidean space.

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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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## 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.

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## Independent set (graph theory)

In graph theory, an independent set or stable set is a set of vertices in a graph, no two of which are adjacent.

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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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## 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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## Intersection

In mathematics, the intersection of two or more objects is another, usually "smaller" object.

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## Iterative method

In computational mathematics, an iterative method is a mathematical procedure that uses an initial guess 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.

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## Java (programming language)

Java is a general-purpose computer-programming language that is concurrent, class-based, object-oriented, and specifically designed to have as few implementation dependencies as possible.

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## Jiří Matoušek (mathematician)

Jiří (Jirka) Matoušek (10 March 1963 – 9 March 2015) was a Czech mathematician working in computational geometry and algebraic topology.

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## Job shop scheduling

Job shop scheduling or the job-shop problem (JSP) is an optimization problem in computer science and operations research in which jobs are assigned to resources at particular times.

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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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## 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 and their applications to problems of heat transfer and vibrations.

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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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## 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.

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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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## 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 equation

In mathematics, a linear equation is an equation that may be put in the form where x_1, \ldots, x_n are the variables or unknowns, and c, a_1, \ldots, a_n are coefficients, which are often real numbers, but may be parameters, or even any expression that does not contain the unknowns.

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## Linear form

In linear algebra, a linear functional or linear form (also called a one-form or covector) is a linear map from a vector space to its field of scalars.

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## Linear inequality

In mathematics a linear inequality is an inequality which involves a linear function.

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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 (programming language)

Lingo is a verbose object-oriented (OO) scripting language developed by John H. Thompson for use in Adobe Director (formerly Macromedia Director).

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## Loss function

In mathematical optimization, statistics, econometrics, decision theory, machine learning and computational neuroscience, a loss function or cost 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.

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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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## Maple (software)

Maple is a symbolic and numeric computing environment, and is also a multi-paradigm programming language.

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## Mark Overmars

Markus Hendrik "Mark" Overmars (born 29 September 1958 in Zeist, Netherlands) is a Dutch computer scientist and teacher of game programming known for his game development application Game Maker.

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## Matching (graph theory)

In the mathematical discipline of graph theory, a matching or independent edge set in a graph is a set of edges without common vertices.

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## Mathcad

Mathcad is computer software primarily intended for the verification, validation, documentation and re-use of engineering calculations.

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## Mathematical model

A mathematical model is a description of a system using mathematical concepts and language.

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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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## MATLAB

MATLAB (matrix laboratory) is a multi-paradigm numerical computing environment and proprietary programming language developed by MathWorks.

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## Matrix (mathematics)

In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

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## Maxima and minima

In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema) or on the entire domain of a function (the global or absolute extrema).

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## Maximum principle

In mathematics, the maximum principle is a property of solutions to certain partial differential equations, of the elliptic and parabolic types.

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## Michael Garey

Michael Randolph Garey is a computer science researcher, and co-author (with David S. Johnson) of Computers and Intractability: A Guide to the Theory of NP-completeness.

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## Microeconomics

Microeconomics (from Greek prefix mikro- meaning "small") 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.

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## Microsoft Excel

Microsoft Excel is a spreadsheet developed by Microsoft for Windows, macOS, Android and iOS.

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## Minkowski addition

In geometry, the Minkowski sum (also known as dilation) 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, i.e., the set Analogously, the Minkowski difference (or geometric difference) is defined as It is important to note that in general A - B\ne A+(-B).

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## MINTO

MINTO (Mixed Integer Optimizer) is an integer programming solver which uses branch and bound algorithm.

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## MOSEK

MOSEK is a software package for the solution of linear, mixed-integer linear, quadratic, mixed-integer quadratic, quadratically constraint, conic and convex nonlinear mathematical optimization problems.

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## Multiple discovery

The concept of multiple discovery (also known as simultaneous invention) is the hypothesis that most scientific discoveries and inventions are made independently and more or less simultaneously by multiple scientists and inventors.

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## NAG Numerical Library

The NAG Numerical Library is a software product developed and sold by The Numerical Algorithms Group.

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## Narendra Karmarkar

Narendra Krishna Karmarkar (born 1957) is an Indian mathematician, who developed Karmarkar's algorithm.

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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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## NMath Stats

NMath Stats is a statistical package for the Microsoft.NET Framework.

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## New Year

New Year is the time or day at which a new calendar year begins and the calendar's year count increments by one.

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## New Year's Day

New Year's Day, also called simply New Year's or New Year, is observed on January 1, the first day of the year on the modern Gregorian calendar as well as the Julian calendar.

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## New Year's Eve

In the Gregorian calendar, New Year's Eve (also known as Old Year's Day or Saint Sylvester's Day in many countries), the last day of the year, is on 31 December which is the seventh day of Christmastide.

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## Nobel Memorial Prize in Economic Sciences

The Nobel Memorial Prize in Economic Sciences (officially Sveriges riksbanks pris i ekonomisk vetenskap till Alfred Nobels minne, or the Swedish National Bank's Prize in Economic Sciences in Memory of Alfred Nobel), commonly referred to as the Nobel Prize in Economics, is an award for outstanding contributions to the field of economics, and generally regarded as the most prestigious award for that field.

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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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## NP-hardness

NP-hardness (''n''on-deterministic ''p''olynomial-time hardness), in computational complexity theory, is the defining property of a class of problems that are, informally, "at least as hard as the hardest problems in NP".

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## Numerical Algorithms Group

The Numerical Algorithms Group (NAG) is a software company which provides methods for the solution of mathematical and statistical problems, and offers services to users of High performance computing (HPC) systems.

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## Observable universe

The observable universe is a spherical region of the Universe comprising all matter that can be observed from Earth at the present time, because electromagnetic radiation from these objects has had time to reach Earth since the beginning of the cosmological expansion.

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## Odysseus

Odysseus (Ὀδυσσεύς, Ὀδυσεύς, Ὀdysseús), also known by the Latin variant Ulysses (Ulixēs), is a legendary Greek king of Ithaca and the hero of Homer's epic poem the Odyssey.

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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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## P (complexity)

In computational complexity theory, P, also known as PTIME or DTIME(nO(1)), is a fundamental complexity class.

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## Packing problems

Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects together into containers.

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## Permissive software licence

A permissive software license, sometimes also called BSD-like or BSD-style license, is a free software software license with minimal requirements about how the software can be redistributed.

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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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## 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.

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## 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 lead to the greatest profit.

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## Proprietary software

Proprietary software is non-free computer software for which the software's publisher or another person retains intellectual property rights—usually copyright of the source code, but sometimes patent rights.

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## Pyomo

Pyomo is a collection of Python software packages for formulating optimization models.

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## Python (programming language)

Python is an interpreted high-level programming language for general-purpose programming.

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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 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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## R (programming language)

R is a programming language and free software environment for statistical computing and graphics that is supported by the R Foundation for Statistical Computing.

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## Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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## Routing

Routing is the process of selecting a path for traffic in a network, or between or across multiple networks.

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## SAS (software)

SAS (previously "Statistical Analysis System") is a software suite developed by SAS Institute for advanced analytics, multivariate analyses, business intelligence, data management, and predictive analytics.

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## Scheduling (production processes)

Scheduling is the process of arranging, controlling and optimizing work and workloads in a production process or manufacturing process.

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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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## 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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## Set cover problem

The set cover problem is a classical question in combinatorics, computer science and complexity theory.

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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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## Simplex algorithm

In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming.

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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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## Soviet Union

The Soviet Union, officially the Union of Soviet Socialist Republics (USSR) was a socialist state in Eurasia that existed from 1922 to 1991.

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## Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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## Stephen Smale

Stephen Smale (born July 15, 1930) is an American mathematician from Flint, Michigan.

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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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## Submodular set function

In mathematics, a submodular set function (also known as a submodular function) is a set function whose value, informally, has the property that the difference in the incremental value of the function that a single element makes when added to an input set decreases as the size of the input set increases.

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## The Mathematical Intelligencer

The Mathematical Intelligencer is a mathematical journal published by Springer Verlag that aims at a conversational and scholarly tone, rather than the technical and specialist tone more common among academic journals.

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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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## Tjalling Koopmans

Tjalling Charles Koopmans (August 28, 1910 – February 26, 1985) was a Dutch American mathematician and economist.

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## TOMLAB

The TOMLAB Optimization Environment is a modeling platform for solving applied optimization problems in MATLAB.

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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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## Transpose

In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal, that is it switches the row and column indices of the matrix by producing another matrix denoted as AT (also written A′, Atr, tA or At).

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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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## Unit cube

A unit cube, more formally a cube of side 1, is a cube whose sides are 1 unit long.

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## Variable (computer science)

In computer programming, a variable or scalar is a storage location (identified by a memory address) paired with an associated symbolic name (an identifier), which contains some known or unknown quantity of information referred to as a value.

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## Vector space

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.

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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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## VisSim

VisSim is a visual block diagram language for simulation of dynamical systems and model based design of embedded systems.

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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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## Wolfram Mathematica

Wolfram Mathematica (usually termed Mathematica) is a modern technical computing system spanning most areas of technical computing — including neural networks, machine learning, image processing, geometry, data science, visualizations, and others.

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## World War II

World War II (often abbreviated to WWII or WW2), also known as the Second World War, was a global war that lasted from 1939 to 1945, although conflicts reflecting the ideological clash between what would become the Allied and Axis blocs began earlier.

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## Worst-case complexity

In computer science, the worst-case complexity (usually denoted in asymptotic notation) measures the resources (e.g. running time, memory) an algorithm requires in the worst-case.

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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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## .NET Framework

.NET Framework (pronounced dot net) is a software framework developed by Microsoft that runs primarily on Microsoft Windows.

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## 2018

2018 has been designated as the third International Year of the Reef by the International Coral Reef Initiative.

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## 2019

2019 (MMXIX) will be a common year starting on Tuesday of the Gregorian calendar, the 2019th year of the Common Era (CE) and Anno Domini (AD) designations, the 19th year of the 3rd millennium, the 19th year of the 21st century, and the 10th and last year of the 2010s decade.

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## Redirects here:

0-1 integer program, 0-1 integer programming, 0-1 integer programs, 0-1 linear programming, 0–1 integer program, 1-0 linear programming, Algorithms for linear programming, Applications of linear programming, Binary integer program, Binary integer programming, Binary integer programs, Complementary slackness, Integer linear program, Integer linear programs, Integer programs, Integral linear program, Integral polyhedron, Integral polytope, LP duality, LP problem, Linear Programming, Linear optimisation, Linear optimization, Linear problem, Linear program, Linear programme, Linear programmer, Linear programmers, Linear programming algorithms, Linear programming duality, Linear programming problem, Linear programs, Lp solve, Mixed integer linear programming, Mixed integer program, Mixed integer programming, Mixed integer programs.

## References

[1] https://en.wikipedia.org/wiki/Linear_programming