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Linear programming: History, Works, Standards & Applications

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).

Language: English [EN]
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Linear programming topic overview

The analysis highlights History, Works, Standards and Applications as prominent areas in the source structure around Linear programming.

Related topics
116
Source areas
12
Connected nodes
128
Extracted relationships
322
Concept neighborhoods
60
Bridge connections
128

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Overview · 50 topics
History · 16 topics
Integer unknowns · 11 topics
Theory · 8 topics
Algorithms · 5 topics
Duality · 5 topics
Open problems and recent work · 5 topics
Integral linear programs · 4 topics
Solvers and scripting (programming) languages · 4 topics
Uses · 4 topics
Augmented form (slack form) · 2 topics
Standard form · 2 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

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

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Linear programming connects Entity context

The extracted context around Linear programming shows recurring relationship patterns in the source. For example, 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 Another extracted example is 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. Use these groups to spot repeated connection types before inspecting the individual relationships.

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

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

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

Linear programming relationships Subject–Predicate–Object triples

TTTA extracted 322 structured relationships around Linear programming. Examples in this analysis include Linear programming → is a → special case of mathematical programming and costs → instance of → Linear programming proved invaluable in optimizing these processes while considering critical constraints. The table shows each extracted connection, where it came from and its confidence.

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

Related concept clusters Concept neighborhoods

The concept neighborhoods around Linear programming bring nearby vocabulary together. In this analysis, examples include Programming, Problem and Problems. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Linear programming
    • Programming
    • Problem
    • Problems
    • Integer
    • Programs
    • Optimization
    • Program
    • Algorithm
    • Solution
    • Method
    • Theory
    • Simplex
  • linear programming
    • Programming
    • Problem
    • Problems
    • Integer
    • Programs
    • Optimization
    • Algorithms
    • Theory
    • Program
    • Algorithm
    • Solution
    • Method
  • linear relationships
    • Programming
    • Problem
    • Problems
    • Integer
    • Programs
    • Optimization
    • Program
    • Algorithm
    • Solution
    • Method
    • Theory
    • Simplex
  • linear
    • Programming
    • Problem
    • Problems
    • Integer
    • Programs
    • Optimization
    • Program
    • Algorithm
    • Solution
    • Method
    • Theory
    • Simplex
  • objective function
    • Function
    • Objective
    • Value
    • Mathbf
    • Displaystyle
    • Optimal
    • Polytope
    • Feasible
    • Solution
    • Point
    • Constraints
    • Problems
  • linear equality
    • Programming
    • Problem
    • Problems
    • Integer
    • Programs
    • Optimization
    • Program
    • Algorithm
    • Solution
    • Method
    • Theory
    • Simplex
  • linear inequality
    • Programming
    • Problem
    • Problems
    • Integer
    • Programs
    • Optimization
    • Program
    • Algorithm
    • Solution
    • Method
    • Theory
    • Simplex
  • constraints
    • Variables
    • Set
    • Function
    • Lp
    • Feasible
    • Matrix
    • Form
    • Number
    • Polytope
    • Objective
    • Solution
    • Problems

Connections between topic areas Semantic bridges

For Linear programming, one of the stronger structural bridges in this analysis connects Linear programming with Overview. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Linear programming — Overview · splits 78 ⟂ 51
Linear programming — History · splits 112 ⟂ 17
Linear programming — Integer unknowns · splits 117 ⟂ 12
Linear programming — Theory · splits 120 ⟂ 9
Linear programming — Duality · splits 123 ⟂ 6
Linear programming — Algorithms · splits 123 ⟂ 6
Linear programming — Open problems and recent work · splits 123 ⟂ 6
Linear programming — Uses · splits 124 ⟂ 5
Linear programming — Integral linear programs · splits 124 ⟂ 5
Linear programming — Solvers and scripting (programming) languages · splits 124 ⟂ 5
Linear programming — Standard form · splits 126 ⟂ 3
Linear programming — Augmented form (slack form) · splits 126 ⟂ 3

Map overview Semantic statistics

Linear programming

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

Source & methodology

TTTA analyzes the structure around Linear programming to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as History, Works, Standards & Applications, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Linear programming · EN edition · Analysis: TopicsToTalkAbout

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