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Perturbation Analysis of Optimization Problems

  • J. Frédéric Bonnans
  • Alexander Shapiro

Part of the Springer Series in Operations Research book series (ORFE)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. J. Frédéric Bonnans, Alexander Shapiro
    Pages 1-7
  3. J. Frédéric Bonnans, Alexander Shapiro
    Pages 8-145
  4. J. Frédéric Bonnans, Alexander Shapiro
    Pages 146-259
  5. J. Frédéric Bonnans, Alexander Shapiro
    Pages 260-400
  6. J. Frédéric Bonnans, Alexander Shapiro
    Pages 401-526
  7. J. Frédéric Bonnans, Alexander Shapiro
    Pages 527-569
  8. J. Frédéric Bonnans, Alexander Shapiro
    Pages 570-582
  9. Back Matter
    Pages 583-601

About this book

Introduction

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.

Keywords

Optimal control linear optimization nonlinear optimization optimization statistics

Authors and affiliations

  • J. Frédéric Bonnans
    • 1
  • Alexander Shapiro
    • 2
  1. 1.INRIA-RocquencourtDomaine de VoluceauLe Chesnay CedexFrance
  2. 2.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1394-9
  • Copyright Information Springer-Verlag New York 2000
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7129-1
  • Online ISBN 978-1-4612-1394-9
  • Series Print ISSN 1431-8598
  • Series Online ISSN 2197-1773
  • Buy this book on publisher's site