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Everything about Linear programming
Method to solve optimization problems
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome in a mathematical model whose requirements and objective are represented by linear relationships. Linear programming is a special case of mathematical programming. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Linear programmingA 5-minute orientation
- Skim a recent paper: Trajectory Optimization for High-Speed Trains via a Mixed Integer Linear Programming ApproachInfluential work since 2022
- Pick up a classic book: Operations researchThe most-reprinted book on the subject
- Read the landmark paper: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programmingCited 8,521 times
- Go sideways: Simplex algorithmA closely related topic
- Go sideways: Basic feasible solutionA closely related topic
📖 Definitions
Noun The branch of mathematics concerned with the minimization or maximization of a linear function of several variables and inequalities; used in many branches of industry to minimize costs or maximize production.
🏆 Landmark papers (most cited)
On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
Decoding by Linear Programming
A generalization of the retention index system including linear temperature programmed gas—liquid partition chromatography
Linear Programming
Bilevel linear programming
Linear multiplicative programming
Grey linear programming
Multiobjective linear programming
🆕 Influential since 2022
Trajectory Optimization for High-Speed Trains via a Mixed Integer Linear Programming Approach
Data-Driven Event-Triggered Adaptive Dynamic Programming Control for Nonlinear Systems With Input Saturation
Two-Level Linear Relaxation Method for Generalized Linear Fractional Programming
Multidimensional solution of fuzzy linear programming
Bi-objective multistage stochastic linear programming
📚 Books worth reading
Operations researchHamdy A. Taha · 1971
An introduction to management scienceDavid Ray Anderson · 1976
Linear programmingRobert J. Vanderbei · 1996
Civil and environmental systems engineeringCharles ReVelle, Charles S. Revelle · 1996
Linear programmingSaul I. Gass · 1964- 📕Linear programming and network flowsMokhtar S. Bazaraa · 1990
Data Envelopment AnalysisSubhash C. Ray · 2004
Linear and integer programmingGerard Sierksma · 1996
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Simplex algorithm In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is an algorithm for linear programming. The name of the algorithm is derived…
- Basic feasible solution In the theory of linear programming, a basic feasible solution (BFS) is a solution with a minimal set of non-zero variables. Geometrically, each BFS corresponds…
- 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.…
- Integer programming An integer programming, also known as integer optimization, problem is a mathematical optimization or feasibility program in which some or all of the variables…
- Mathematical optimization Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria…
- 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…
- List of numerical analysis topics This is a list of numerical analysis topics. Validated numerics Iterative method Rate of convergence — the speed at which a convergent sequence approaches…
- Feasible region In mathematical optimization and computer science, a feasible region, feasible set, or solution space is the set of all possible points (sets of values…