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From Convexity to Nonconvexity

  • Book
  • © 2001

Overview

Editors:
  1. R. P. Gilbert

    1. University of Delaware, USA

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  2. P. D. Panagiotopoulos
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  3. P. M. Pardalos

    1. University of Florida, USA

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

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Table of contents (27 chapters)

  1. Front Matter

    Pages i-xi
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  2. A Survey of Basic Mathematical Results for Frictional Contact Problems

    • Lars-Erik Andersson, Anders Klarbring
    Pages 1-14

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

    • Siegfried Carl
    Pages 15-28

  4. A Survey on Nonsmooth Critical Point Theory and Applications

    • Marco Degiovanni
    Pages 29-42

  5. Exhaustive Families of Approximations Revisited

    • V. F. Demyanov, A. M. Rubinov
    Pages 43-50

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

    • ZdzisÅ‚aw Denkowski
    Pages 51-65

  7. Duality in Nonconvex Finite Deformation Theory: A Survey and Unified Approach

    • David Yang Gao
    Pages 67-83

  8. Contact Problems in Multibody Dynamics a Review

    • Friedrich Pfeiffer, Christoph Glocker
    Pages 85-109

  9. Hyperbolic Hemivariational Inequality and Nonlinear Wave Equation with Discontinuities

    • D. Goeleven, D. Motreanu
    Pages 111-122

  10. A Survey on Time-Integration Algorithms for Convex and Nonconvex Elastoplasticity

    • Klaus Hackl
    Pages 123-136

  11. Contact Stress Optimization

    • J. Haslinger
    Pages 137-145

  12. Recent Results in Contact Problems with Coulomb Friction

    • Jiří JaruÅ¡ek, Christof Eck
    Pages 147-160

  13. Polarization Fields in the Variational Analysis of the Linear Plezoelectric Problem

    • P. Bisegna, F. Maceri
    Pages 161-175

  14. Surver of the Methods for Nonsmooth Optimization

    • M. M. Mäkelä
    Pages 177-191

  15. Hemivariational Inequalities and Hysteresis

    • M. Miettinen
    Pages 193-206

  16. Non Convex Aspects of Dynamics with Impact

    • Lætitia Paoli, Michelle Schatzman
    Pages 207-222

  17. On Global Properties of D.C.Functions

    • L. N. Polyakova
    Pages 223-231

  18. Existence Results for Variational-Hemivariational Inequalities: A F.E.Browder Technique

    • G. Dinca, G. Pop
    Pages 233-241

  19. Perturbations of Eigenvalue Problems with Constraints for Hemivariational Inequalities

    • Vicentiu D. Rădulescu
    Pages 243-253

  20. Implicit Variational Inequalities Arising in Frictional Unilateral Contact Mechanics: Analysis and Numerical Solution of Quasistatic Problems

    • Marius Cocu, Michel Raous
    Pages 255-267
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Keywords

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.

Editors and Affiliations

  • University of Delaware, USA

    R. P. Gilbert

  • University of Florida, USA

    P. M. Pardalos

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