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Simplex algorithm

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

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Overview

History

Standard form

Simplex tableau

Pivot operations

Algorithm

Advanced topics

Other algorithms

Linear-fractional programming

Works cited

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Simplex algorithm

Nodes72
Edges71
Triples107
Avg. degree1.97
Density0.027778
Components1

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Simplex algorithm

Top relations

related to External links · 30
Simplex algorithm → An Introduction, Colorado, Daniel Izquierdo, Denver, Georgia Institute, Greenberg, Harvey, Juan José Ruiz, Klee, Linear Programming, Linear Programming Problems, M-method, Mathstools Simplex Calculator, Method, Minty Polytope Shows Exponential, Málaga, Online Simplex Solver, PDF, PHPSimplex, Simplex Method
related to Further reading · 24
Simplex algorithm → Algorithms, Charles, Clifford Stein, Cormen, Frederick, Gerald, Hillier, Introduction, ISBN, Leiserson, Lieberman, McGraw-Hill, MIT Press, Operations Research, Optimization, Prentice Hall, Rivest, Ronald, Second Edition, Section
related to Degeneracy: stalling and cycling · 12
Simplex algorithm → Another, Basic, Bland's, Cunningham's, History-based, If, In, Padberg, When, While, Worse, Zadeh's
related to Finding an initial canonical tableau · 8
Simplex algorithm → Columns, If, In, Phase, Phase II, So, The, This
related to Efficiency in practice · 6
Simplex algorithm → Analyzing, Another, Baire, Indeed, The, This
related to Implementation · 6
Simplex algorithm → Both, In, It, The, These, This
related to Linear-fractional programming · 5
Simplex algorithm → In, In LP, LFP, Linear, LP
related to Algorithm · 3
Simplex algorithm → If, Let, The
related to overview · 2
Simplex algorithm → The, There

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Important terminology

simplex linear algorithm objective variables function solution variable basic pivot program feasible column tableau displaystyle value row problem method form

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
the second oneinstance ofappears0.80text
some authors refer to the variable introduced as a surplus variable.Thirdinstance ofappears0.80text
each unrestricted variable is eliminated from the linear programinstance ofappears0.80text
Devex algorithm.If none of the entries in the objective row is negative then no choice of entering variable can be madeinstance ofand the choice of which one to add to the set of basic variables is guided by one of several entering variable choice rules0.80text
the solution is in fact at the maximuminstance ofand the choice of which one to add to the set of basic variables is guided by one of several entering variable choice rules0.80text
Fourierinstance ofthe criss-cross algorithm never cycles on linear programs.History-based pivot rules such as Zadeh's rule and Cunningham's rule also try to circumvent the issue of stalling and c…0.80text
Zadeh's ruleinstance ofthe criss-cross algorithm never cycles on linear programs.History-based pivot rules0.80text
Cunningham's rule also try to circumvent the issue of stallinginstance ofthe criss-cross algorithm never cycles on linear programs.History-based pivot rules0.80text
cycling by keeping track of how often particular variables are being usedinstance ofthe criss-cross algorithm never cycles on linear programs.History-based pivot rules0.80text
then favor such variables that have been used least ofteninstance ofthe criss-cross algorithm never cycles on linear programs.History-based pivot rules0.80text
Fourierinstance ofEfficiency in the worst caseThe simplex method is remarkably efficient in practice and was a great improvement over earlier methods0.80text
Simplex algorithmrelated to AlgorithmLet0.60section

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