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Minimax Theory and Applications

  • Book
  • © 1998

Overview

Editors:
  1. Biagio Ricceri

    1. Department of Mathematics, University of Catania, Catania, Italy

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  2. Stephen Simons

    1. Department of Mathematics, University of California at Santa Barbara, Santa Barbara, USA

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    You can also search for this editor in PubMed   Google Scholar

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

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Table of contents (18 chapters)

  1. Front Matter

    Pages i-xi
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  2. Nonlinear Two Functions Minimax Theorems

    • Cao-Zong Cheng, Bor-Luh Lin
    Pages 1-20

  3. Weakly Upward-Downward Minimax Theorem

    • Cao-Zong Cheng, Bor-Luh Lin, Feng-Shuo Yu
    Pages 21-28

  4. A Two-Function Minimax Theorem

    • Antonia Chinnì
    Pages 29-33

  5. Generalized Fixed-Points and Systems of Minimax Inequalities

    • Paul Deguire
    Pages 35-40

  6. A Minimax Inequality for Marginally Semicontinuous Functions

    • Gabriele H. Greco, Maria Pia Moschen
    Pages 41-51

  7. On Variational Minimax Problems under Relaxed Coercivity Assumptions

    • Joachim Gwinner
    Pages 53-69

  8. A Topological Investigation of the Finite Intersection Property

    • Charles D. Horvath
    Pages 71-90

  9. Minimax Results and Randomization for Certain Stochastic Games

    • Albrecht Irle
    Pages 91-103

  10. Intersection Theorems, Minimax Theorems and Abstract Connectedness

    • Jürgen Kindler
    Pages 105-120

  11. K-K-M-S Type Theorems in Infinite Dimensional Spaces

    • Hidetoshi Komiya
    Pages 121-134

  12. Hahn-Banach Theorems for Convex Functions

    • Marc Lassonde
    Pages 135-145

  13. Two Functions Generalization of Horvath’s Minimax Theorem

    • Bor-Luh Lin, Feng-Shuo Yu
    Pages 147-156

  14. Some Remarks on a Minimax Formulation of a Variational Inequality

    • Giandomenico Mastroeni
    Pages 157-166

  15. Network Analysis

    • Michael M. Neumann, Maria Victoria Velasco
    Pages 167-189

  16. On a Topological Minimax Theorem and its Applications

    • Biagio Ricceri
    Pages 191-216

  17. Three Lectures on Minimax and Monotonicity

    • Stephen Simons
    Pages 217-240

  18. Fan’s Existence Theorem for Inequalities Concerning Convex Functions and Its Applications

    • Wataru Takahashi
    Pages 241-260

  19. An Algorithm for the Multi-Access Channel Problem

    • Peng-Jung Wan, Ding-Zu Du, Panos M. Pardalos
    Pages 261-270

  20. Back Matter

    Pages 271-274
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Keywords

About this book

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.

Editors and Affiliations

  • Department of Mathematics, University of Catania, Catania, Italy

    Biagio Ricceri

  • Department of Mathematics, University of California at Santa Barbara, Santa Barbara, USA

    Stephen Simons

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