Perturbation Analysis of Optimization Problems (original) (raw)
Overview
Authors:
- J. Frédéric Bonnans
- INRIA-Rocquencourt, Domaine de Voluceau, Le Chesnay Cedex, France
- Alexander Shapiro
- School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, USA
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About this book
The main subject of this book is perturbation analysis of continuous optimization problems. In the last two decades considerable progress has been made in that area, and it seems that it is time now to present a synthetic view of many important results that apply to various classes of problems. The model problem that is considered throughout the book is of the form (P) Min/(x) subjectto G(x) E K. xeX Here X and Y are Banach spaces, K is a closed convex subset of Y, and / : X -+ IR and G : X -+ Y are called the objective function and the constraint mapping, respectively. We also consider a parameteriZed version (P ) of the above u problem, where the objective function / (x, u) and the constraint mapping G(x, u) are parameterized by a vector u varying in a Banach space U. Our aim is to study continuity and differentiability properties of the optimal value v(u) and the set S(u) of optimal solutions of (P ) viewed as functions of the parameter vector u.
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Table of contents (7 chapters)
Introduction
- J. Frédéric Bonnans, Alexander Shapiro
Pages 1-7
- J. Frédéric Bonnans, Alexander Shapiro
Authors and Affiliations
INRIA-Rocquencourt, Domaine de Voluceau, Le Chesnay Cedex, France
J. Frédéric Bonnans
School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, USA
Alexander Shapiro
Bibliographic Information
- Book Title: Perturbation Analysis of Optimization Problems
- Authors: J. Frédéric Bonnans, Alexander Shapiro
- Series Title: Springer Series in Operations Research and Financial Engineering
- DOI: https://doi.org/10.1007/978-1-4612-1394-9
- Publisher: Springer New York, NY
- eBook Packages: Springer Book Archive
- Copyright Information: Springer Science+Business Media New York 2000
- Hardcover ISBN: 978-0-387-98705-7Published: 11 May 2000
- Softcover ISBN: 978-1-4612-7129-1Published: 15 November 2013
- eBook ISBN: 978-1-4612-1394-9Published: 22 November 2013
- Series ISSN: 1431-8598
- Series E-ISSN: 2197-1773
- Edition Number: 1
- Number of Pages: XVIII, 601
- Topics: Calculus of Variations and Optimal Control; Optimization, Systems Theory, Control