Minimax Theory And Applications
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Author | : Biagio Ricceri |
Publisher | : Springer Science & Business Media |
Total Pages | : 278 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 940159113X |
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.
Author | : Ding-Zhu Du |
Publisher | : Springer Science & Business Media |
Total Pages | : 300 |
Release | : 2013-12-01 |
Genre | : Computers |
ISBN | : 1461335574 |
Techniques and principles of minimax theory play a key role in many areas of research, including game theory, optimization, and computational complexity. In general, a minimax problem can be formulated as min max f(x, y) (1) ",EX !lEY where f(x, y) is a function defined on the product of X and Y spaces. There are two basic issues regarding minimax problems: The first issue concerns the establishment of sufficient and necessary conditions for equality minmaxf(x,y) = maxminf(x,y). (2) "'EX !lEY !lEY "'EX The classical minimax theorem of von Neumann is a result of this type. Duality theory in linear and convex quadratic programming interprets minimax theory in a different way. The second issue concerns the establishment of sufficient and necessary conditions for values of the variables x and y that achieve the global minimax function value f(x*, y*) = minmaxf(x, y). (3) "'EX !lEY There are two developments in minimax theory that we would like to mention.
Author | : Paul H. Rabinowitz |
Publisher | : American Mathematical Soc. |
Total Pages | : 110 |
Release | : 1986-07-01 |
Genre | : Mathematics |
ISBN | : 0821807153 |
The book provides an introduction to minimax methods in critical point theory and shows their use in existence questions for nonlinear differential equations. An expanded version of the author's 1984 CBMS lectures, this volume is the first monograph devoted solely to these topics. Among the abstract questions considered are the following: the mountain pass and saddle point theorems, multiple critical points for functionals invariant under a group of symmetries, perturbations from symmetry, and variational methods in bifurcation theory. The book requires some background in functional analysis and differential equations, especially elliptic partial differential equations. It is addressed to mathematicians interested in differential equations and/or nonlinear functional analysis, particularly critical point theory.
Author | : Michel Willem |
Publisher | : Springer Science & Business Media |
Total Pages | : 168 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461241464 |
Many boundary value problems are equivalent to Au=O (1) where A : X --+ Y is a mapping between two Banach spaces. When the problem is variational, there exists a differentiable functional rand inf.
Author | : Haim Brézis |
Publisher | : |
Total Pages | : 0 |
Release | : 2003 |
Genre | : Chebyshev approximation |
ISBN | : 9781571461094 |
This volume contains both survey and creative papers dealing with Morse theory, minimax theory, iteration theory of Maslov-type index and critical minimization problems. The book particularly emphasizes applications to nonlinear differential equations.
Author | : Aleksandr Petrovich Korostelev |
Publisher | : American Mathematical Soc. |
Total Pages | : 258 |
Release | : 2011 |
Genre | : Mathematics |
ISBN | : 0821852833 |
iPositive Give a man a fish, he eats for a day, but if you teach him to fish, you feed him for life. Such is the approach of iPositive. One day at the gym doesnt make a person fit for life; its a consistent dedication to getting the body in shape that eventually yields results. The lessons in iPositive work in much the same way: They challenge the reader to work to keep the mind in shape. The book is a powerful guide to personal happiness through positivity. Its concepts provide empowerment to overcome self-doubt, disbelief and inferiority complexes in order to transcend the negativity in life. iPositive is geared toward helping individuals become more focused on the things they most want in life, like happiness, love and success, or banish anchors that may be weighting them down, like stress, smoking or excess weight. The book gives readers the practical means to become more focused on those things they want in life, and serves as an inspirational manual for a life of fulfillment, and strength in body, mind and spirit.
Author | : Frank C. Zagare |
Publisher | : SAGE |
Total Pages | : 100 |
Release | : 1984-07 |
Genre | : Mathematics |
ISBN | : 9780803920507 |
Professor Zagare provides methods for analysing the structure of the game; considers zero and nonzero-sum games and the fundamental 'minimax theorem'; and investigates games with more than two players, including the possibility of coalitions between players.
Author | : Kim C. Border |
Publisher | : Cambridge University Press |
Total Pages | : 144 |
Release | : 1985 |
Genre | : Business & Economics |
ISBN | : 9780521388085 |
This book explores fixed point theorems and its uses in economics, co-operative and noncooperative games.
Author | : Panos M. Pardalos |
Publisher | : Springer Science & Business Media |
Total Pages | : 872 |
Release | : 2008-07-02 |
Genre | : Mathematics |
ISBN | : 0387772472 |
This comprehensive work examines important recent developments and modern applications in the fields of optimization, control, game theory and equilibrium programming. In particular, the concepts of equilibrium and optimality are of immense practical importance affecting decision-making problems regarding policy and strategies, and in understanding and predicting systems in different application domains, ranging from economics and engineering to military applications. The book consists of 29 survey chapters written by distinguished researchers in the above areas.
Author | : Len Fisher |
Publisher | : Basic Books |
Total Pages | : 280 |
Release | : 2008-11-04 |
Genre | : Science |
ISBN | : 0786726938 |
Praised by Entertainment Weekly as “the man who put the fizz into physics,” Dr. Len Fisher turns his attention to the science of cooperation in his lively and thought-provoking book. Fisher shows how the modern science of game theory has helped biologists to understand the evolution of cooperation in nature, and investigates how we might apply those lessons to our own society. In a series of experiments that take him from the polite confines of an English dinner party to crowded supermarkets, congested Indian roads, and the wilds of outback Australia, not to mention baseball strategies and the intricacies of quantum mechanics, Fisher sheds light on the problem of global cooperation. The outcomes are sometimes hilarious, sometimes alarming, but always revealing. A witty romp through a serious science, Rock, Paper, Scissors will both teach and delight anyone interested in what it what it takes to get people to work together.