Minimax Theory and Applications: (26 Nonconvex Optimization and Its Applications)

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.

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 Stochastic 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.