Nonconvex Optimization and Its Applications

From Convexity to Nonconvexity

Editors: Gilbert, R.P., Panagiotopoulos, Panagiotis D., Pardalos, Panos (Eds.)

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About this book

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.

Table of contents (27 chapters)

Table of contents (27 chapters)
  • A Survey of Basic Mathematical Results for Frictional Contact Problems

    Pages 1-14

    Andersson, Lars-Erik (et al.)

  • A Survey of Recent Results on the Enclosure and Extremality of Solutions for Quasilinear Hemivariational Inequalities

    Pages 15-28

    Carl, Siegfried

  • A Survey on Nonsmooth Critical Point Theory and Applications

    Pages 29-42

    Degiovanni, Marco

  • Exhaustive Families of Approximations Revisited

    Pages 43-50

    Demyanov, V. F. (et al.)

  • A Survey on Optimal Shape Design Problems for Systems Described by Partial Differential Equations and Hemivariational Inequalities

    Pages 51-65

    Denkowski, Zdzisław

Buy this book

eBook 93,08 €
price for Spain (gross)
  • ISBN 978-1-4613-0287-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 166,39 €
price for Spain (gross)
  • ISBN 978-0-7923-7144-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 114,39 €
price for Spain (gross)
  • ISBN 978-1-4613-7979-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
From Convexity to Nonconvexity
Editors
  • R.P. Gilbert
  • Panagiotis D. Panagiotopoulos
  • Panos Pardalos
Series Title
Nonconvex Optimization and Its Applications
Series Volume
55
Copyright
2001
Publisher
Springer US
Copyright Holder
Kluwer Academic Publishers
eBook ISBN
978-1-4613-0287-2
DOI
10.1007/978-1-4613-0287-2
Hardcover ISBN
978-0-7923-7144-1
Softcover ISBN
978-1-4613-7979-9
Series ISSN
1571-568X
Edition Number
1
Number of Pages
XII, 396
Topics