Linear programming : foundations and extensions
著者
書誌事項
Linear programming : foundations and extensions
（International series in operations research & management science, 37）
Kluwer Academic, c2001
2nd ed
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注記
Includes bibliographical references (p. [435]-442) and index
内容説明・目次
内容説明
This is an introduction to the field of optimization. The book emphasizes constrained optimization, beginning with a substantial treatment of linear programming, and proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. Specific examples and concrete algorithms precede more abstract topics. Topics are clearly developed with a large number of numerical examples worked out in detail. Moreover, the book underscores the purpose of optimization: to solve practical problems on a computer. Accordingly, the book is co-ordinated with free efficient C programs that implement the major algorithms studied.
目次
Preface. Preface to 2nd Edition. Part 1: Basic Theory -- The Simplex Method and Duality. 1. Introduction. 2. The Simplex Method. 3. Degeneracy. 4. Efficiency of the Simplex Method. 5. Duality Theory. 6. The Simplex Method in Matrix Notation. 7. Sensitivity and Parametric Analysis. 8. Implementation Issues. 9. Problems in General Form. 10. Convex Analysis. 11. Game Theory. 12. Regression. Part 2: Network-Type Problems. 13. Network Flow Problems. 14. Applications. 15. Structural Optimization. Part 3: Interior-Point Methods. 16. The Central Path. 17. A Path-Following Method. 18. The KKT System. 19. Implementation Issues. 20. The Affine-Scaling Method. 21. The Homogeneous Self-Dual Method. Part 4: Extensions. 22. Integer Programming. 23. Quadratic Programming. 24. Convex Programming. Appendix. Answers to Selected Exercises. Bibliography. Index.
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