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Numerical Optimization

Theoretical and Practical Aspects

  • J. Frédéric Bonnans
  • J. Charles Gilbert
  • Claude Lemaréchal
  • Claudia A. Sagastizábal
Textbook

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Preliminaries

    1. Front Matter
      Pages 1-1
    2. J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal
      Pages 3-20
  3. Unconstrained Problems

    1. Front Matter
      Pages 21-23
    2. J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal
      Pages 25-35
    3. J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal
      Pages 37-50
    4. J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal
      Pages 51-66
    5. J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal
      Pages 67-76
    6. J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal
      Pages 77-90
  4. Nonsmooth Optimization

    1. Front Matter
      Pages 91-93
    2. J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal
      Pages 95-100
    3. J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal
      Pages 101-116
    4. J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal
      Pages 117-136
    5. J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal
      Pages 137-148
  5. Newton’s Methods in Constrained Optimization

    1. Front Matter
      Pages 149-155
    2. J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal
      Pages 157-168
    3. J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal
      Pages 169-202
    4. J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal
      Pages 203-215
    5. J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal
      Pages 217-233
    6. J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal
      Pages 235-264
    7. J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal
      Pages 265-281
  6. Interior-Point Algorithms for Linear and Quadratic Optimization

    1. Front Matter
      Pages 283-289
    2. J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal
      Pages 291-306
    3. J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal
      Pages 307-328
    4. J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal
      Pages 329-344
    5. J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal
      Pages 345-356
    6. J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal
      Pages 357-366
    7. J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal
      Pages 367-382
    8. J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal
      Pages 383-388
    9. J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal
      Pages 389-395
  7. Back Matter
    Pages 397-423

About this book

Introduction

Starting with illustrative real-world examples, this book exposes in a tutorial way algorithms for numerical optimization: fundamental ones (Newtonian methods, line-searches, trust-region, sequential quadratic programming, etc.), as well as more specialized and advanced ones (nonsmooth optimization, decomposition techniques, and interior-point methods). Most of these algorithms are explained in a detailed manner, allowing straightforward implementation. Theoretical aspects are addressed with care, often using minimal assumptions.

The present version contains substantial changes with respect to the first edition. Part I on unconstrained optimization has been completed with a section on quadratic programming. Part II on nonsmooth optimization has been thoroughly reorganized and expanded. In addition, nontrivial application problems have been inserted, in the form of computational exercises. These should help the reader to get a better understanding of optimization methods beyond their abstract description, by addressing important features to be taken into account when passing to implementation of any numerical algorithm.

This level of detail is intended to familiarize the reader with some of the crucial questions of numerical optimization: how algorithms operate, why they converge, difficulties that may be encountered and their possible remedies.

 

Keywords

Optimization algorithms algorithms interior-point methods linear optimization nonsmooth optimization optimization sequential quadratic programming

Authors and affiliations

  • J. Frédéric Bonnans
    • 1
  • J. Charles Gilbert
    • 1
  • Claude Lemaréchal
    • 2
  • Claudia A. Sagastizábal
    • 3
  1. 1.INRIA RocquencourtLe ChesnayFrance
  2. 2.INRIA Rhône-AlpesMontbonnot, Saint IsmierFrance
  3. 3.IMPAJardim Botânico, Rio de Janeiro-RJBrazil

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-05078-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-00191-1
  • Online ISBN 978-3-662-05078-1
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site
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