Nonlinear Programming and Variational Inequality Problems

A Unified Approach

  • Michael Patriksson

Part of the Applied Optimization book series (APOP, volume 23)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Michael Patriksson
    Pages 1-38
  3. Michael Patriksson
    Pages 39-56
  4. Michael Patriksson
    Pages 57-93
  5. Michael Patriksson
    Pages 95-133
  6. Michael Patriksson
    Pages 211-251
  7. Back Matter
    Pages 277-336

About this book

Introduction

Since I started working in the area of nonlinear programming and, later on, variational inequality problems, I have frequently been surprised to find that many algorithms, however scattered in numerous journals, monographs and books, and described rather differently, are closely related to each other. This book is meant to help the reader understand and relate algorithms to each other in some intuitive fashion, and represents, in this respect, a consolidation of the field. The framework of algorithms presented in this book is called Cost Approxi­ mation. (The preface of the Ph.D. thesis [Pat93d] explains the background to the work that lead to the thesis, and ultimately to this book.) It describes, for a given formulation of a variational inequality or nonlinear programming problem, an algorithm by means of approximating mappings and problems, a principle for the update of the iteration points, and a merit function which guides and monitors the convergence of the algorithm. One purpose of this book is to offer this framework as an intuitively appeal­ ing tool for describing an algorithm. One of the advantages of the framework, or any reasonable framework for that matter, is that two algorithms may be easily related and compared through its use. This framework is particular in that it covers a vast number of methods, while still being fairly detailed; the level of abstraction is in fact the same as that of the original problem statement.

Keywords

Approximation algorithms linear optimization nonlinear optimization optimization programming

Authors and affiliations

  • Michael Patriksson
    • 1
  1. 1.Chalmers University of TechnologyGothenburgSweden

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-2991-7
  • Copyright Information Springer-Verlag US 1999
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-4806-9
  • Online ISBN 978-1-4757-2991-7
  • Series Print ISSN 1384-6485
  • About this book