Optimization theory

著者

書誌事項

Optimization theory

by Hubertus Th. Jongen, Klaus Meer, Eberhard Triesch

Kluwer Academic, c2004

  • : hbk

大学図書館所蔵 件 / 全13件

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注記

Includes bibliographical references and index

内容説明・目次

内容説明

This volume provides a comprehensive introduction to the theory of (deterministic) optimization. It covers both continuous and discrete optimization. This allows readers to study problems under different points-of-view, which supports a better understanding of the entire field. Many exercises are included to increase the reader's understanding.

目次

  • Preface.- PART I. CONTINUOUS OPTIMIZATION.- 1. Optimality Criteria on Simple Regions.- 2. Constraints, Lagrange Function, Optimality.- 3. Parametric Aspects, Semi-Infinite Optimization.- 4. Convex Functions, Duality, Separation Theorem.- 5. Linear Inequalities, Constraint Qualifications.- 6. Linear Programming: The Simplex Method.- 7. The Ellipsoid Method.- 8. Karmarkar's Method for Linear Programming.- 9. Order of Convergence, Steepest Descent.- 10. Conjugate Direction, Variable Metric.- 11. Penalty-, Barrier-, Multiplier-, IP-Methods.- 12. Search Methods without Derivatives.- 13. One-Dimensional Minimization.- PART II. DISCRETE OPTIMIZATION.- 14. Graphs and Networks.- 15. Flows in Networks.- 16. Applications of the Max-Flow Min-Cut Theorem.- 17. Integer Linear Programming.- 18. Computability
  • the Turing machine.- 19. Complexity theory.- 20. Reducibility and NP-completeness.- 21. Some NP-completeness results.- 22. The Random Access Machine.- 23. Complexity Theory over the Real Numbers.- 24. Approximating NP-hard Problems.- 25. Approximation Algorithms for TSP.- 26. Approximation algorithms for Bin Packing.- 27. A FPTAS for Knapsack.- 28. Miscellaneous.- Index.- Index of Symbols.- References.

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