Linear programming and Simplex algorithm

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Difference between Linear programming and Simplex algorithm

Linear programming vs. Simplex algorithm

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

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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Algorithm

In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.

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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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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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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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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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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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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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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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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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Karmarkar's algorithm

Karmarkar's algorithm is an algorithm introduced by Narendra Karmarkar in 1984 for solving linear programming problems.

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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 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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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-fractional programming

In mathematical optimization, linear-fractional programming (LFP) is a generalization of linear programming (LP).

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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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Narendra Karmarkar

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

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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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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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Polytope

In elementary geometry, a polytope is a geometric object with "flat" sides.

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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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