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From Convexity to Nonconvexity

  • R. P. Gilbert
  • P. D. Panagiotopoulos
  • P. M. Pardalos

Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 55)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Lars-Erik Andersson, Anders Klarbring
    Pages 1-14
  3. V. F. Demyanov, A. M. Rubinov
    Pages 43-50
  4. Friedrich Pfeiffer, Christoph Glocker
    Pages 85-109
  5. J. Haslinger
    Pages 137-145
  6. Jiří Jarušek, Christof Eck
    Pages 147-160
  7. M. Miettinen
    Pages 193-206
  8. Lætitia Paoli, Michelle Schatzman
    Pages 207-222
  9. L. N. Polyakova
    Pages 223-231
  10. Mirosław Przeworski, Dariusz Zagrodny
    Pages 363-380
  11. Michele Carriero, Antonio Leaci, Franco Tomarelli
    Pages 381-392
  12. Back Matter
    Pages 393-395

About this book

Introduction

This collection of papers is dedicated to the memory of Gaetano Fichera, a great mathematician and also a good friend to the editors. Regrettably it took an unusual amount of time to bring this collection out. This was primarily due to the fact that the main editor who had collected all of the materials, for this volume, P. D. Panagiotopoulos, died unexpectedly during the period when we were editing the manuscript. The other two editors in appreciation of Panagiotopoulos' contribution to this field, believe it is therefore fitting that this collection be dedicated to his memory also. The theme of the collection is centered around the seminal research of G. Fichera on the Signorini problem. Variants on this idea enter in different ways. For example, by bringing in friction the problem is no longer self-adjoint and the minimization formulation is not valid. A large portion of this collection is devoted to survey papers concerning hemivariational methods, with a main point of its application to nonsmooth mechanics. Hemivariational inequali­ ties, which are a generalization of variational inequalities, were pioneered by Panagiotopoulos. There are many applications of this theory to the study of non convex energy functionals occurring in many branches of mechanics. An area of concentration concerns contact problems, in particular, quasistatic and dynamic contact problems with friction and damage. Nonsmooth optimization methods which may be divided into the main groups of subgradient methods and bundle methods are also discussed in this collection.

Keywords

algorithms approximation contact mechanics deformation design duality dynamics eigenvalue problem electricity function mechanics operator optimization plasticity theorem

Editors and affiliations

  • R. P. Gilbert
    • 1
  • P. D. Panagiotopoulos
  • P. M. Pardalos
    • 2
  1. 1.University of DelawareUSA
  2. 2.University of FloridaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-0287-2
  • Copyright Information Springer-Verlag US 2001
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-7979-9
  • Online ISBN 978-1-4613-0287-2
  • Series Print ISSN 1571-568X
  • Buy this book on publisher's site