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Integer and Combinatorial Optimization
- Author / Creator
- Available as
- Online
- Summary
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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 be...
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
Details
- Format
- Books
- Language
- English
- Contributors
- Publication
-
- 1st ed
- Hoboken : Wiley, 2014
- Physical Details
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- 1 online resource (783 p.)
- ISBNs
- 9781118626863, 1118626869, 9781118627372, 1118627377, 9781118627259, 1118627253, 0471359432, 1322094713
- Description based upon print version of record.
- English
- Cover ; Title Page ; Copyright ; Preface ; Contents ; Part I: Foundations ; I.1 The Scope of Integer and Combinatorial Optimization ; 1. Introduction ; 2. Modeling with Binary Variables I: Knapsack, Assignmentand Matching, Covering, Packing and Partitioning ; The 0-1 Knapsack Problem ; The Assignment and Matching Problems ; Set-covering, Set-packing, and Set-partitioning Problems ; 3. Modeling with Binary Variables II: Facility Location, Fixed-charge Network Flow, and Traveling Salesman ; Facility Location Problems ; The Fixed-charge Network Flow Problem ; The Traveling Salesman Problem
- 4. Modeling with Binary Variables III: Nonlinear Functions and Disjunctive ConstraintsPiecewise Linear Functions ; Disjunctive Constraints ; A Scheduling Problem ; 5. Choices in Model Formulation ; 6. Preprocessing ; Tightening Bounds ; Adding Logical Inequalities, Fixing Variables, and Removing Redundant Constraints ; 7. Notes ; Section I.1.1 ; Sections I.1.2-I.1.4 ; Section I.1.5 ; Section I.1.6 ; 8. Exercises ; I.2: Linear Programming ; 1. Introduction ; 2. Duality ; 3. The Primal and Dual Simplex Algorithms ; Bases and Basic Solutions ; Changing the Basis ; Primal Simplex Algorithm
- Dual Simplex Algorithm Dual Simplex Algorithm (phase 2) ; The Simplex Algorithm with Simple Upper Bounds ; Addition of Constraints or Variables ; 4. Subgradient Optimization ; The Subgradient Algorithm for (4.1) ; 5. Notes ; Sections I.2.1-i.2.3. ; Section I.2.4 ; I.3: Graphs and Networks ; 1. Introduction ; 2. The Minimum-weight or Shortest-path Problem ; Dijkstra''s Minimum-weight Path Algorithm ; Bellman-ford Minimum-weight Path Algorithm ; 3. The Minimum-weight Spanning Tree Problem ; Algorithm for Constructing a Spanning Tree ; 4. The Maximum-flow and Minimum-cut Problems
- Augmenting Path Algorithm 5. The Transportation Problem: A Primal-dual Algorithm ; Primal-dual Algorithm for the Transportation Problem ; Minimum-cost Path Augmentation Algorithm ; 6. A Primal Simplex Algorithm for Network Flow Problems ; 7. Notes ; Section I.3.1 ; Section I.3.2 ; Section I.3.3 ; Section I.3.4 ; Section I.3.5 ; Section I.3.6 ; 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 ; 5. Polarity
- 6. Polyhedral Ties Between Linear and Integer Programs 7. Notes ; Sections I.4.1-I.4.4 ; Section I.4.5 ; Section I.4.6 ; 8. Exercises ; 1.5: 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 ; Certificates of Feasibility, the Class Np, and Nondeterministic Algorithms ; 6. The Most Difficult Np Problems: the Class Np ; 7. Complexity and Polyhedra ; 8. Notes ; Sections I.5.1 and I.5.2
- Section I.5.3