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 thus an opportunity for popularizing these techniques among researchers involved in other sciences, including users of optimization in a wide sense, in mechanics, physics, statistics, finance and economics. Of use to research professionals, including graduate students at an advanced level.
Perturbation Analysis of Optimization Problems
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4.0 out of 5 stars
Excellent book for continuous optimization,
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This review is from: Perturbation Analysis of Optimization Problems (Hardcover)
I think this work is a very complete source of tools for continuous optimization.The abstract setting allows the consideration and analysis of many different problems like semi definite and semi infinite programming, optimal control and variational inequalities. This generality calls for important results in functional analysis that are well documented in the book. Many concrete applications of the theory are included and a special chapter is dedicated to review the bibliography related with all the covered themes. I think it is a must have in the area.
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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second order growth condition, second order approximation set, second order tangent sets, strict constraint qualification, outer second order, second order regularity, constraint qualification for the problem, nonpositive valued functions, linearized variational inequality, inner tangent cones, composite optimization problem, fixed feasible set, quadratic growth condition, nonnegative linear form, optimal value val, strict complementarity condition, following second order conditions, conic linear problem, corresponding discretized problem, linearized generalized equations, order subderivatives, first order differentiability properties, first order optimality system, nonempty relative interior, directional regularity Key Phrases - Capitalized Phrases (CAPs): (learn more)
Generalized Open Mapping Theorem New!
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second order growth condition, second order approximation set, second order tangent sets, strict constraint qualification, outer second order, second order regularity, constraint qualification for the problem, nonpositive valued functions, linearized variational inequality, inner tangent cones, composite optimization problem, fixed feasible set, quadratic growth condition, nonnegative linear form, optimal value val, strict complementarity condition, following second order conditions, conic linear problem, corresponding discretized problem, linearized generalized equations, order subderivatives, first order differentiability properties, first order optimality system, nonempty relative interior, directional regularity Key Phrases - Capitalized Phrases (CAPs): (learn more)
Generalized Open Mapping Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 26
books:
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37
books
cite this book:
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- Mathematical Programming: Structures and Algorithms by Jeremy F. Shapiro in Back Matter (1), Back Matter (2), and Back Matter (3)
- Convex Analysis (Princeton Landmarks in Mathematics and Physics) by Ralph Tyrell Rockafellar in Back Matter (1), and Back Matter (2)
- Optimization Theory by Hubertus Th. Jongen in Back Matter (1), and Back Matter (2)
- Nonlinear Functional Analysis and Applications by Louis B. Rall in Back Matter
- Topics in Matrix Analysis by Roger A. Horn in Back Matter
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- Handbooks in Operations Research and Management Science: Stochastic Programming (Hanbooks in Operations Research and Management Series) by A. Ruszczynski on page 63, page 423, and page 478
- Multivalued Analysis and Nonlinear Programming Problems with Perturbations (Nonconvex Optimization and Its Applications (closed)) by B. Luderer in Back Matter (1), and Back Matter (2)
- Finite-Dimensional Variational Inequalities and Complementarity Problems I by Francisco Facchinei in Front Matter, and Back Matter
- Recent Advances in Optimization (Lecture Notes in Economics and Mathematical Systems) by Alberto Seeger on page 145
- Stochastic-Process Limits by Ward Whitt in Front Matter
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