| Description |
1 online resource (783 pages) |
| Contents |
Title; Copyright Page; Dedication; Preface; PART I. FOUNDATIONS; I.1 The Scope of Integer and Combinatorial Optimization; 1. Introduction; 2. Modeling with Binary Variables I: Knapsack, Assignment and Matching, Covering, Packing and Partitioning; 3. Modeling with Binary Variables II: Facility Location, Fixed-Charge Network Flow, and Traveling Salesman; 4. Modeling with Binary Variables III: Nonlinear Functions and Disjunctive Constraints; 5. Choices in Model Formulation; 6. Preprocessing; 7. Notes; 8. Exercises; I.2 Linear Programming; 1. Introduction; 2. Duality |
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3. The Primal and Dual Simplex Algorithms4. Subgradient Optimization; 5. Notes; I.3 Graphs and Networks; 1. Introduction; 2. The Minimum-Weight or Shortest-Path Problem; 3. The Minimum-Weight Spanning Tree Problem; 4. The Maximum-Flow and Minimum-Cut Problems; 5. The Transportation Problem: A Primal-Dual Algorithm; 6. A Primal Simplex Algorithm for Network Flow Problems; 7. Notes; I.4 Polyhedral Theory; 1. Introduction and Elementary Linear Algebra; 2. Definitions of Polyhedra and Dimension; 3. Describing Polyhedra by Facets; 4. Describing Polyhedra by Extreme Points and Extreme Rays |
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5. Polarity6. Polyhedral Ties Between Linear and Integer Programs; 7. Notes; 8. Exercises; I.5 Computational Complexity; 1. Introduction; 2. Measuring Algorithm Efficiency and Problem Complexity; 3. Some Problems Solvable in Polynomial Time; 4. Remarks on 0-1 and Pure-Integer Programming; 5. Nondeterministic Polynomial-Time Algorithms and NP Problems; 6. The Most Difficult NP Problems: The Class NPC; 7. Complexity and Polyhedra; 8. Notes; 9. Exercises; I.6 Polynomial-Time Algorithms for Linear Programming; 1. Introduction; 2. The Ellipsoid Algorithm |
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3. The Polynomial Equivalence of Separation and Optimization4. A Projective Algorithm; 5. A Strongly Polynomial Algorithm for Combinatorial Linear Programs; 6. Notes; I.7 Integer Lattices; 1. Introduction; 2. The Euclidean Algorithm; 3. Continued Fractions; 4. Lattices and Hermite Normal Form; 5. Reduced Bases; 6. Notes; 7. Exercises; PART II. GENERAL INTEGER PROGRAMMING; II. 1 The Theory of Valid Inequalities; 1. Introduction; 2. Generating All Valid Inequalities; 3. Gomory's Fractional Cuts and Rounding; 4. Superadditive Functions and Valid Inequalities |
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5. A Polyhedral Description of Superadditive Valid Inequalities for Independence Systems6. Valid Inequalities for Mixed-Integer Sets; 7. Superadditivity for Mixed-Integer Sets; 8. Notes; 9. Exercises; II. 2 Strong Valid Inequalities and Facets for Structured Integer Programs; 1. Introduction; 2. Valid Inequalities for the 0-1 Knapsack Polytope; 3. Valid Inequalities for the Symmetric Traveling Salesman Polytope; 4. Valid Inequalities for Variable Upper-Bound Flow Models; 5. Notes; 6. Exercises; II. 3 Duality and Relaxation; 1. Introduction; 2. Duality and the Value Function |
| Summary |
Rave reviews for INTEGER AND COMBINATORIAL OPTIMIZATION""This book provides an excellent introduction and survey of traditional fields of combinatorial optimization ... It is indeed one of the best and most complete texts on combinatorial optimization ... available. [And] with more than 700 entries, [it] has quite an exhaustive reference list.""--Optima""A unifying approach to optimization problems is to formulate them like linear programming problems, while restricting some or all of the variables to the integers. This book is an encyclopedic resource for such formulations, as well as for |
| Notes |
English |
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Print version record |
| Subject |
Combinatorial optimization.
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Integer programming.
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Mathematical optimization.
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Combinatorial optimization
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Integer programming
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Mathematical optimization
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| Form |
Electronic book
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| Author |
Nemhauser, George L
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| ISBN |
9781118627259 |
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1118627253 |
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9781118627372 |
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1118627377 |
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1118626869 |
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9781118626863 |
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