Minimax Theory and Applications

  • Biagio Ricceri
  • Stephen Simons

Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 26)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Cao-Zong Cheng, Bor-Luh Lin
    Pages 1-20
  3. Cao-Zong Cheng, Bor-Luh Lin, Feng-Shuo Yu
    Pages 21-28
  4. Antonia Chinnì
    Pages 29-33
  5. Gabriele H. Greco, Maria Pia Moschen
    Pages 41-51
  6. Marc Lassonde
    Pages 135-145
  7. Bor-Luh Lin, Feng-Shuo Yu
    Pages 147-156
  8. Michael M. Neumann, Maria Victoria Velasco
    Pages 167-189
  9. Stephen Simons
    Pages 217-240
  10. Peng-Jung Wan, Ding-Zu Du, Panos M. Pardalos
    Pages 261-270
  11. Back Matter
    Pages 271-274

About this book

Introduction

The present volume contains the proceedings of the workshop on "Minimax Theory and Applications" that was held during the week 30 September - 6 October 1996 at the "G. Stampacchia" International School of Mathematics of the "E. Majorana" Centre for Scientific Cul­ ture in Erice (Italy) . The main theme of the workshop was minimax theory in its most classical meaning. That is to say, given a real-valued function f on a product space X x Y , one tries to find conditions that ensure the validity of the equality sup inf f(x,y) = inf sup f(x, y). yEY xEX xEX yEY This is not an appropriate place to enter into the technical details of the proofs of minimax theorems, or into the history of the contribu­ tions to the solution of this basic problem in the last 7 decades. But we do want to stress its intrinsic interest and point out that, in spite of its extremely simple formulation, it conceals a great wealth of ideas. This is clearly shown by the large variety of methods and tools that have been used to study it. The applications of minimax theory are also extremely interesting. In fact, the need for the ability to "switch quantifiers" arises in a seemingly boundless range of different situations. So, the good quality of a minimax theorem can also be judged by its applicability. We hope that this volume will offer a rather complete account of the state of the art of the subject.

Keywords

Operator theory Sim algorithms calculus functional analysis game theory optimization

Editors and affiliations

  • Biagio Ricceri
    • 1
  • Stephen Simons
    • 2
  1. 1.Department of MathematicsUniversity of CataniaCataniaItaly
  2. 2.Department of MathematicsUniversity of California at Santa BarbaraSanta BarbaraUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-9113-3
  • Copyright Information Springer Science+Business Media B.V. 1998
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-5030-4
  • Online ISBN 978-94-015-9113-3
  • Series Print ISSN 1571-568X
  • About this book
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