Linear optimization and approximation

Cover......Page 1
Title Page......Page 4
Copyright Page......Page 5
Preface......Page 6
Table of Contents......Page 10
1. Optimization Problems......Page 12
2. Some Mathematical Prerequisites......Page 16
3. Linear Optimization Problems......Page 21
4. Duality Lemma and Dual Problem......Page 31
5. State Diagrams and Duality Gaps......Page 41
6. Uniform Approximation......Page 48
7. Polynomial Approximation......Page 57
CHAPTER IV. DUALITY THEORY......Page 69
8. Geometric Interpretation of the Dual Problem S......Page 19
9. Solvability of the Dual Problem......Page 80
10. Separation Theorem and Duality......Page 86
11. Supporting Hyperplanes and Duality......Page 93
CHAPTER V. THE SIMPLEX ALGORITHM......Page 103
12. Basic Solutions and the Exchange Step......Page 104
13. The Simplex Algorithm and Discretization......Page 116
14. Stable Variants of the Simplex Algorithm......Page 126
15. Calculating a Basic Solution......Page 139
CHAPTER VII. A GENERAL THREE-PHASE ALGORITHM......Page 145
16. Nonlinear Systems Derived From Optimality   Conditions......Page 146
17. A General Computational Scheme......Page 152
18. General Properties of Chebyshev Systems......Page 164
19. One-sided Approximation and Generalized  Quadrature Rules of the Gaussian Type......Page 169
20. Computing the Best Approximation in the  Uniform Norm......Page 179
21. A Control Problem with Distributed Parameters......Page 186
22. Operator Equations of Monotonic Type......Page 192
23. An Air Pollution Abatement Problem......Page 195
24. Nonlinear Semi-Infinite Programs......Page 199
References......Page 204
Index......Page 207