Optimization Theory (Hardcover)

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.