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Perturbation Analysis of Optimization Problems Book

Perturbation Analysis of Optimization Problems
Perturbation Analysis of Optimization Problems, A presentation of general results for discussing local optimality and computation of the expansion of value function and approximate solution of optimization problems, followed by their application to various fields, from physics to economics. The book is, Perturbation Analysis of Optimization Problems has a rating of 5 stars
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Perturbation Analysis of Optimization Problems, A presentation of general results for discussing local optimality and computation of the expansion of value function and approximate solution of optimization problems, followed by their application to various fields, from physics to economics. The book is, Perturbation Analysis of Optimization Problems
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  • Perturbation Analysis of Optimization Problems
  • Written by author J. Frederic Bonnans
  • Published by Springer-Verlag New York, LLC, May 2000
  • A presentation of general results for discussing local optimality and computation of the expansion of value function and approximate solution of optimization problems, followed by their application to various fields, from physics to economics. The book is
  • This book presents general results for discussing local optimality and computation of the expansion of value function and approximate solution of optimization problems. These results may be applied to various fields, from physics to economics, as various
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Basic Notation
1Introduction1
2Background Material8
2.1Basic Functional Analysis8
2.2Directional Differentiability and Tangent Cones34
2.3Elements of Multifunctions Theory54
2.4Convex Functions74
2.5Duality Theory95
3Optimality Conditions146
3.1First Order Optimality Conditions147
3.2Second Order Necessary Conditions162
3.3Second Order Sufficient Conditions186
3.4Specific Structures217
3.5Nonisolated Minima245
4Stability and Sensitivity Analysis260
4.1Stability of the Optimal Value and Optimal Solutions261
4.2Directional Regularity266
4.3First Order Differentiability Analysis of the Optimal Value Function271
4.4Quantitative Stability of Optimal Solutions and Lagrange Multipliers286
4.5Directional Stability of Optimal Solutions303
4.6Quantitative Stability Analysis by a Reduction Approach314
4.7Second Order Analysis in Lipschitz Stable Cases323
4.8Second Order Analysis in Holder Stable Cases347
4.9Additional Results365
4.10Second Order Analysis in Functional Spaces386
5Additional Material and Applications401
5.1Variational Inequalities401
5.2Nonlinear Programming436
5.3Semi-definite Programming470
5.4Semi-infinite Programming496
6Optimal Control527
6.1Introduction527
6.2Linear and Semilinear Elliptic Equations528
6.3Optimal Control of a Semilinear Elliptic Equation539
6.4The Obstacle Problem558
7Bibliographical Notes570
References583
Index595


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Perturbation Analysis of Optimization Problems, A presentation of general results for discussing local optimality and computation of the expansion of value function and approximate solution of optimization problems, followed by their application to various fields, from physics to economics. The book is, Perturbation Analysis of Optimization Problems

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Perturbation Analysis of Optimization Problems, A presentation of general results for discussing local optimality and computation of the expansion of value function and approximate solution of optimization problems, followed by their application to various fields, from physics to economics. The book is, Perturbation Analysis of Optimization Problems

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