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Minimax Theory and Applications (Paperback, Softcover reprint of the original 1st ed. 1998)
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Minimax Theory and Applications (Paperback, Softcover reprint of the original 1st ed. 1998)
Series: Nonconvex Optimization and Its Applications, 26
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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."
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