Minimax Theory and Applications / Edition 1

by Biagio Ricceri, Stephen Simons

Overview

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 contributions 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.

Product Details

ISBN-13:	9789048150304
Publisher:	Springer Netherlands
Publication date:	12/09/2010
Series:	Nonconvex Optimization and Its Applications , #26
Edition description:	Softcover reprint of the original 1st ed. 1998
Pages:	274
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

Nonlinear Two Functions Minimax Theorems.- Weakly Upward-Downward Minimax Theorem.- A Two-Function Minimax Theorem.- Generalized Fixed-Points and Systems of Minimax Inequalities.- A Minimax Inequality for Marginally Semicontinuous Functions.- On Variational Minimax Problems under Relaxed Coercivity Assumptions.- A Topological Investigation of the Finite Intersection Property.- Minimax Results and Randomization for Certain Shastic Games.- Intersection Theorems, Minimax Theorems and Abstract Connectedness.- K-K-M-S Type Theorems in Infinite Dimensional Spaces.- Hahn-Banach Theorems for Convex Functions.- Two Functions Generalization of Horvath’s Minimax Theorem.- Some Remarks on a Minimax Formulation of a Variational Inequality.- Network Analysis.- On a Topological Minimax Theorem and its Applications.- Three Lectures on Minimax and Monotonicity.- Fan’s Existence Theorem for Inequalities Concerning Convex Functions and its Applications.- An Algorithm for the Multi-Access Channel Problem.- Author Index.

Editorial Reviews

Concentrating mainly on classical minimax theory, the 71 papers from the September-October, 1996 workshop in Erice, Italy elucidate current trends in the basic theory, the role of connectedness as it eclipses that of convexity, and applications concerning game theory, integral functions, and monotone operators. A sampling of specific topics includes: weakly upward- downward theorems, a two-function theorem, generalized fixed- points and systems of minimax inequalities, minimax results for certain stochastic games, K-K-M-S type theorems in infinite dimensional spaces, network analysis, and applications of a topological minimax theorem. Intended for graduate students and researchers in mathematical programming, functional analysis, topology, operator theory, and game theory. Author index only. Annotation c. by Book News, Inc., Portland, Or.

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