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Perturbation Analysis of Optimization Problems : Springer Series in Operations Research and Financial Engineering - J. F. Bonnans

Perturbation Analysis of Optimization Problems

Springer Series in Operations Research and Financial Engineering

Hardcover Published: 11th May 2000
ISBN: 9780387987057
Number Of Pages: 601

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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 examples in the book show. Therefore, the book is an opportunity for popularizing these techniques among researchers involved in other sciences. Consequently the readership should be not only researchers in the field of optimization, nonlinear programming and optimal control, but also users of optimization in a wide sense, in mechanics (elasticity and plasticity theory), physics, statistics, finance and economics. The book will be useful to research professionals, including graduate students at an advanced level.

Basic Notation
Introductionp. 1
Background Materialp. 8
Basic Functional Analysisp. 8
Directional Differentiability and Tangent Conesp. 34
Elements of Multifunctions Theoryp. 54
Convex Functionsp. 74
Duality Theoryp. 95
Optimality Conditionsp. 146
First Order Optimality Conditionsp. 147
Second Order Necessary Conditionsp. 162
Second Order Sufficient Conditionsp. 186
Specific Structuresp. 217
Nonisolated Minimap. 245
Stability and Sensitivity Analysisp. 260
Stability of the Optimal Value and Optimal Solutionsp. 261
Directional Regularityp. 266
First Order Differentiability Analysis of the Optimal Value Functionp. 271
Quantitative Stability of Optimal Solutions and Lagrange Multipliersp. 286
Directional Stability of Optimal Solutionsp. 303
Quantitative Stability Analysis by a Reduction Approachp. 314
Second Order Analysis in Lipschitz Stable Casesp. 323
Second Order Analysis in Holder Stable Casesp. 347
Additional Resultsp. 365
Second Order Analysis in Functional Spacesp. 386
Additional Material and Applicationsp. 401
Variational Inequalitiesp. 401
Nonlinear Programmingp. 436
Semi-definite Programmingp. 470
Semi-infinite Programmingp. 496
Optimal Controlp. 527
Introductionp. 527
Linear and Semilinear Elliptic Equationsp. 528
Optimal Control of a Semilinear Elliptic Equationp. 539
The Obstacle Problemp. 558
Bibliographical Notesp. 570
Referencesp. 583
Indexp. 595
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387987057
ISBN-10: 0387987053
Series: Springer Series in Operations Research and Financial Engineering
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 601
Published: 11th May 2000
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.9 x 17.3  x 3.8
Weight (kg): 1.11