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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 is a special case of mathematical programming (also known as mathematical optimization).

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Overview

History

Uses

Standard form

Augmented form (slack form)

Duality

Theory

Algorithms

Open problems and recent work

Integer unknowns

Integral linear programs

Solvers and scripting (programming) languages

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Linear programming

Nodes129
Edges128
Triples322
Avg. degree1.98
Density0.015504
Components1

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Linear programming

Top relations

related to References · 128
Linear programming → Academic Press, Activity Analysis, Advances, Albert, Algorithms, Allocation, Annals, Applications, Approximation Algorithms, Average, Beasley, Benders, BF02614325, Bland, Borgwardt, California, Chapman-Hall, Christos, Cite, CiteSeerX
related to Further reading · 83
Linear programming → A6, Action, Advanced, Alexander Schrijver, Analysis, Berg, Berlin, Bernd, Chapter, Chapters, Combinatorial, Computational Geometry, Computer Exercises, Computers, Cornelis Roos, CRC Press, David, Describes, Diptesh Ghosh, Dmitris Alevras
see also · 17
Linear programming → Abstraction, Algorithm, Branch, Concept, Convex, LFP, Method, Optimization, Periodicity, Problem, Quantitative, Solution, Solving, Statistical, Study, Subfield, Term
related to Example · 12
Linear programming → Every, F1, F2, If, In, Let S1, P1, P2, S2, Suppose, The, This
related to Integer unknowns · 12
Linear programming → BIP, If, ILP, In, IP, Karp's, MILP, MIP, NP-complete, NP-hard, These, This
related to history · 11
Linear programming → American, Fourier, In, Kantorovich, Leonid Kantorovich, Leontief, Motzkin, Soviet, The, Their, Wassily Leontief
related to Ellipsoid algorithm, following Khachiyan · 9
Linear programming → Arkadi Nemirovski, Finally, Leonid Khachiyan, Naum, Shor, The, This, To, Yudin
related to Optimal vertices (and rays) of polyhedra · 9
Linear programming → For, However, Let, LP, Otherwise, The, Then, Thereby, This
related to Integral linear programs · 8
Linear programming → As, Ax, Conversely, Edmonds, Giles, Integral, Likewise, Specifically
related to Uses · 8
Linear programming → Although, Certain, Google, Historically, Likewise, Linear, Many, YouTube

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Important terminology

linear programming algorithm problems problem displaystyle variables simplex dual feasible polytope function algorithms method objective methods optimization integer solution primal

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Linear programmingis aspecial case of mathematical programming0.90text
costsinstance ofLinear programming proved invaluable in optimizing these processes while considering critical constraints0.80text
resource availability.Despite its initial obscurityinstance ofLinear programming proved invaluable in optimizing these processes while considering critical constraints0.80text
the wartime successes propelled linear programming into the spotlightinstance ofLinear programming proved invaluable in optimizing these processes while considering critical constraints0.80text
Linear programminghas methodThe0.60section
Linear programminghas methodHowever0.60section
Linear programminghas methodLP0.60section
Linear programmingrelated to Augmented form (slack form)Linear0.60section
Linear programmingrelated to Augmented form (slack form)This0.60section
Linear programmingrelated to Augmented form (slack form)The0.60section
Linear programmingrelated to DualityEvery0.60section
Linear programmingrelated to DualityIn0.60section

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