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Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods

  • Masao Fukushima
  • Liqun Qi

Part of the Applied Optimization book series (APOP, volume 22)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Regina S. Burachik, Claudia A. Sagastizábal, B. F. Svaiter
    Pages 25-43
  3. Xiaojun Chen, Nami Matsunaga, Tetsuro Yamamoto
    Pages 65-79
  4. Peter W. Christensen, Jong-Shi Pang
    Pages 81-116
  5. Steven P. Dirkse, Michael C. Ferris
    Pages 127-147
  6. Christian Kanzow, Martin Zupke
    Pages 211-233
  7. Patrice Marcotte
    Pages 269-291
  8. Ji-Ming Peng
    Pages 293-316
  9. Alexander M. Rubinov, Bevil Glover
    Pages 335-354
  10. Michael V. Solodov, Benav F. Svaiter
    Pages 355-369
  11. Back Matter
    Pages 443-444

About this book

Introduction

The concept of "reformulation" has long been playing an important role in mathematical programming. A classical example is the penalization technique in constrained optimization that transforms the constraints into the objective function via a penalty function thereby reformulating a constrained problem as an equivalent or approximately equivalent unconstrained problem. More recent trends consist of the reformulation of various mathematical programming prob­ lems, including variational inequalities and complementarity problems, into equivalent systems of possibly nonsmooth, piecewise smooth or semismooth nonlinear equations, or equivalent unconstrained optimization problems that are usually differentiable, but in general not twice differentiable. Because of the recent advent of various tools in nonsmooth analysis, the reformulation approach has become increasingly profound and diversified. In view of growing interests in this active field, we planned to organize a cluster of sessions entitled "Reformulation - Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods" in the 16th International Symposium on Mathematical Programming (ismp97) held at Lausanne EPFL, Switzerland on August 24-29, 1997. Responding to our invitation, thirty-eight people agreed to give a talk within the cluster, which enabled us to organize thirteen sessions in total. We think that it was one of the largest and most exciting clusters in the symposium. Thanks to the earnest support by the speakers and the chairpersons, the sessions attracted much attention of the participants and were filled with great enthusiasm of the audience.

Keywords

Finite Operations Research Operator Variable algorithm algorithms calculus equation function linear optimization mathematical programming modeling optimization programming

Editors and affiliations

  • Masao Fukushima
    • 1
  • Liqun Qi
    • 2
  1. 1.Kyoto UniversityKyotoJapan
  2. 2.The University of New South WalesSydneyAustralia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-6388-1
  • Copyright Information Springer-Verlag US 1999
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-4805-2
  • Online ISBN 978-1-4757-6388-1
  • Series Print ISSN 1384-6485
  • Buy this book on publisher's site
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