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© 2003

Numerical Optimization

Theoretical and Practical Aspects

Benefits

  • Combines mathematical developments, description and analysis of algorithms

  • Selection of algorithms is based on their applicability to real-life problems

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

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

  1. 1.INRIA RocquencourtLe ChesnayFrance
  2. 2.INRIA Rhône-AlpesMontbonnot, Saint IsmierFrance
  3. 3.IMPAJardim Botânico, Rio de Janeiro-RJBrazil

About the authors

The four authors are leading international specialists in various branches of nonlinear optimization (one of them received the Dantzig Prize). They are working - or have worked - at INRIA, the French National Institute for Research in Computer Science and Control, and they also teach in various universities and "Grandes Écoles". All of them continually collaborate with industry on problems dealing with optimization, in fields such as energy management, geoscience, life sciences, etc.

Bibliographic information

Industry Sectors
Electronics
Engineering
Finance, Business & Banking
Law

Reviews

From the reviews of the second edition:

"This volume is a collection of four coordinated monographs on topics in numerical optimization. … the four sections of the book fit together to provide a broad survey of methods for numerical optimization at an advanced level. … this book should be of interest to advanced graduate students and researchers working in numerical optimization." (Brian Borchers, MathDL, March, 2007)

"More realistic application problems are introduced with the emphasis on outlining a typical modeling process in more detail. … the presentation of theoretical results on nonsmooth optimization is reorganized and contains now a new subsection with convergence results. The book provides an excellent basis for studying optimization theory and algorithms, especially for nonsmooth optimization. Additional case studies, availability of computer codes, and exercises improve the understanding of numerical algorithms and the practical problem solving process. In summary, the second edition significantly improves the first one." (Klaus Schittkowski, Zentralblatt MATH, Vol. 1108 (10), 2007)