Mathematical Programming : an Introduction to Optimization.
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| Format: | eBook |
| Language: | English |
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Boca Raton :
Routledge,
2018.
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| Series: | Chapman and Hall/CRC Pure and Applied Mathematics.
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Cover; Half Title; Title Page; Copyright Page; Table of Contents; PREFACE; Chapter 1 AN INTRODUCTION TO MATHEMATICAL PROGRAMMING; 1. The Mathematical Programming Problem; 2. Examples of Mathematical Programming Problems; 4. Post-Optimal Analysis, Parametric Programming, and Stability; 5. Some Historical Comments; References; Chapter 2 SUBSPACES, MATRICES, AFFINE SETS, CONES, CONVEX SETS, AND THE LINEAR PROGRAMMING PROBLEM; 1. A Review of Elementary Linear Algebra; 2. Affine and Convex Sets; 3. The Linear Programming Problem; References; Chapter 3 THE PRIMAL SIMPLEX PROCEDURE.
- 1. The Primal Simplex Procedure2. Artificial Variables and Artificial Cost Coefficients; 3. Artificial Variables and the Two-Phase Method; References; Chapter 4 DUALITY AND THE LINEAR COMPLEMENTARITY PROBLEM; 1. Dual Linear Programming Problems; 2. Interpretation of the Dual Problem (Post-Optimal Analysis); 3. Post-Optimal Analysis; 4. The Dual Simplex Procedure; 5. Complementary Slackness; 6. The Linear Complementarity Problem; 7. Lemke's Complementary Pivoting Algorithm; References; Chapter 5 OTHER SIMPLEX PROCEDURES; 1. The Primal Simplex Tableau Revisited; 2. The Revised Simplex Procedure.
- 3. The Product Form of the Inverse4. The Elimination Form of the Inverse; 5. The Primal-Dual Algorithm; 6. Parametric Linear Programming; 7. Degeneracy and Cycling; 8. Decomposition; 9. Reinversion; References; Chapter 6 NETWORK PROGRAMMING; 1. Linear Network Flow Problems; 2. Some Basic Graph Theory; 3. The Network Simplex Procedure for the Transshipment Problem; 4. The Maximal Flow Problem; 5. Primal Dual Procedures for Network Flow Problems; References; Chapter 7 CONVEX AND CONCAVE FUNCTIONS; 1. Introduction; 2. Convex Functions of One Real Variable; 3. Some Topics from Calculus.
- 4. Convex Functions of Several Variables5. Optimization of Convex Functions; 6. Quasiconvex Functions and Other Generalizations; References; Chapter 8 OPTIMALITY CONDITIONS; 1. Unconstrained Problems; 2. Nonnegative Variables; 3. Equality Constraints; 4. Nonnegative Variables and Equality Constraints; 5. Nonnegative Variables and Inequality Constraints; 6. The Kuhn-Tucker Theorem; References; Chapter 9 SEARCH TECHNIQUES FOR UNCONSTRAINED OPTIMIZATION PROBLEMS; 1. One-Dimensional Linear Search Techniques; 2. Linear Search Techniques by Curve Fitting.
- 3. Linear Search Techniques for Differential Functions by Curve Fitting4. Multidimensional Search Techniques; References; Chapter 10 PENALTY FUNCTION METHODS; 1. Introduction; 2. Barrier Function Methods; 3. The Quadratic Penalty Function Method; References; INDEX.