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Integer programming

About: Integer programming is a research topic. Over the lifetime, 25381 publications have been published within this topic receiving 618828 citations.


Papers
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Book
01 Dec 1986
TL;DR: Introduction and Preliminaries.
Abstract: Introduction and Preliminaries. Problems, Algorithms, and Complexity. LINEAR ALGEBRA. Linear Algebra and Complexity. LATTICES AND LINEAR DIOPHANTINE EQUATIONS. Theory of Lattices and Linear Diophantine Equations. Algorithms for Linear Diophantine Equations. Diophantine Approximation and Basis Reduction. POLYHEDRA, LINEAR INEQUALITIES, AND LINEAR PROGRAMMING. Fundamental Concepts and Results on Polyhedra, Linear Inequalities, and Linear Programming. The Structure of Polyhedra. Polarity, and Blocking and Anti--Blocking Polyhedra. Sizes and the Theoretical Complexity of Linear Inequalities and Linear Programming. The Simplex Method. Primal--Dual, Elimination, and Relaxation Methods. Khachiyana s Method for Linear Programming. The Ellipsoid Method for Polyhedra More Generally. Further Polynomiality Results in Linear Programming. INTEGER LINEAR PROGRAMMING. Introduction to Integer Linear Programming. Estimates in Integer Linear Programming. The Complexity of Integer Linear Programming. Totally Unimodular Matrices: Fundamental Properties and Examples. Recognizing Total Unimodularity. Further Theory Related to Total Unimodularity. Integral Polyhedra and Total Dual Integrality. Cutting Planes. Further Methods in Integer Linear Programming. References. Indexes.

7,005 citations

Book
01 Jan 1988
TL;DR: This chapter discusses the Scope of Integer and Combinatorial Optimization, as well as applications of Special-Purpose Algorithms and Matching.
Abstract: FOUNDATIONS. The Scope of Integer and Combinatorial Optimization. Linear Programming. Graphs and Networks. Polyhedral Theory. Computational Complexity. Polynomial-Time Algorithms for Linear Programming. Integer Lattices. GENERAL INTEGER PROGRAMMING. The Theory of Valid Inequalities. Strong Valid Inequalities and Facets for Structured Integer Programs. Duality and Relaxation. General Algorithms. Special-Purpose Algorithms. Applications of Special- Purpose Algorithms. COMBINATORIAL OPTIMIZATION. Integral Polyhedra. Matching. Matroid and Submodular Function Optimization. References. Indexes.

6,287 citations

Book
01 Jan 1972
TL;DR: The principles of integer programming are directed toward finding solutions to problems from the fields of economic planning, engineering design, and combinatorial optimization as mentioned in this paper, which is a standard of graduate-level courses since 1972.
Abstract: The principles of integer programming are directed toward finding solutions to problems from the fields of economic planning, engineering design, and combinatorial optimization. This highly respected and much-cited text, a standard of graduate-level courses since 1972, presents a comprehensive treatment of the first two decades of research on integer programming.

4,336 citations

Journal ArticleDOI
TL;DR: Four key areas of Integer programming are examined from a framework that links the perspectives of artificial intelligence and operations research, and each has characteristics that appear usefully relevant to developments on the horizon.

3,985 citations

Book
01 Jan 1967
TL;DR: The Simplex Method duality theory and sensitivity analysis for linear programming has been studied extensively in the field of operations research as mentioned in this paper, including the application of queueing theory inventory theory forecasting Markovian decision processes and applications decision analysis simulation.
Abstract: Overview of the operations research modelling approach introduction to linear programming solving linear programming problems - the Simplex Method the theory of the Simplex Method duality theory and sensitivity analysis other algorithms for linear programming the transportation and assignment problems network analysis, including Pert-CPM dynamic programming game theory integer programming non-linear programming Markov chains queueing theory the application of queueing theory inventory theory forecasting Markovian decision processes and applications decision analysis simulation.

3,830 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20242
2023864
20222,002
20211,251
20201,324
20191,455