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The Linearization Method for Constrained Optimization

  • Boris N. Pshenichnyj

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 22)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Boris N. Pshenichnyj
    Pages 1-42
  3. Boris N. Pshenichnyj
    Pages 43-97
  4. Boris N. Pshenichnyj
    Pages 99-141
  5. Back Matter
    Pages 143-150

About this book

Introduction

Techniques of optimization are applied in many problems in economics, automatic control, engineering, etc. and a wealth of literature is devoted to this subject. The first computer applications involved linear programming problems with simp- le structure and comparatively uncomplicated nonlinear pro- blems: These could be solved readily with the computational power of existing machines, more than 20 years ago. Problems of increasing size and nonlinear complexity made it necessa- ry to develop a complete new arsenal of methods for obtai- ning numerical results in a reasonable time. The lineariza- tion method is one of the fruits of this research of the last 20 years. It is closely related to Newton's method for solving systems of linear equations, to penalty function me- thods and to methods of nondifferentiable optimization. It requires the efficient solution of quadratic programming problems and this leads to a connection with conjugate gra- dient methods and variable metrics. This book, written by one of the leading specialists of optimization theory, sets out to provide - for a wide readership including engineers, economists and optimization specialists, from graduate student level on - a brief yet quite complete exposition of this most effective method of solution of optimization problems.

Keywords

Newton's method Newtonsches Verfahren Optimierung von Algorithmen Straffunktion algorithm algorithms economics linear optimization nichtlineare und quadratische Programmierung nonlinear and quadratic programming optimization optimization theory penalty function programming

Authors and affiliations

  • Boris N. Pshenichnyj
    • 1
  1. 1.Institute of Cybernetics of the Academy of the Ukrainian SSRKiev - 207Ukraina, CIS

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-57918-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 1994
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-63401-7
  • Online ISBN 978-3-642-57918-9
  • Series Print ISSN 0179-3632
  • Buy this book on publisher's site
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