Minimax and Applications
Minimax and Applications

Author: Ding-Zhu Du

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 300

ISBN-13: 1461335574

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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.

Minimax Theory and Applications
Minimax Theory and Applications

Author: Biagio Ricceri

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 278

ISBN-13: 940159113X

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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.

Minimax Theorems
Minimax Theorems

Author: Michel Willem

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 168

ISBN-13: 1461241464

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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.

Minimax Methods in Critical Point Theory with Applications to Differential Equations
Minimax Methods in Critical Point Theory with Applications to Differential Equations

Author: Paul H. Rabinowitz

Publisher: American Mathematical Soc.

Published: 1986-07-01

Total Pages: 110

ISBN-13: 0821807153

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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.

An Introduction to Minimax Theorems and Their Applications to Differential Equations
An Introduction to Minimax Theorems and Their Applications to Differential Equations

Author: Maria do Rosário Grossinho

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 279

ISBN-13: 1475733089

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The book is intended to be an introduction to critical point theory and its applications to differential equations. Although the related material can be found in other books, the authors of this volume have had the following goals in mind: To present a survey of existing minimax theorems, To give applications to elliptic differential equations in bounded domains, To consider the dual variational method for problems with continuous and discontinuous nonlinearities, To present some elements of critical point theory for locally Lipschitz functionals and give applications to fourth-order differential equations with discontinuous nonlinearities, To study homoclinic solutions of differential equations via the variational methods. The contents of the book consist of seven chapters, each one divided into several sections. Audience: Graduate and post-graduate students as well as specialists in the fields of differential equations, variational methods and optimization.

Mathematical Statistics
Mathematical Statistics

Author: Aleksandr Petrovich Korostelev

Publisher: American Mathematical Soc.

Published: 2011

Total Pages: 258

ISBN-13: 0821852833

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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.

Minimax
Minimax

Author: Fouad Sabry

Publisher: One Billion Knowledgeable

Published: 2023-06-28

Total Pages: 181

ISBN-13:

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What Is Minimax In artificial intelligence, decision theory, game theory, statistics, and philosophy, minmax is a decision rule that is used to minimize the probable loss for a worst case scenario. When discussing profits, one may often hear the term "maximin" used, which stands for "maximizing the minimum gain." It was initially developed for the theory of several-player zero-sum games, including both the circumstances in which players take alternate movements and those in which they make simultaneous actions. Since then, however, it has been expanded to more complicated games as well as to general decision-making in the presence of uncertainty. How You Will Benefit (I) Insights, and validations about the following topics: Chapter 1: Minimax Chapter 2: Game Theory Chapter 3: Decision Trees Chapter 4: Alpha-Beta Pruning Chapter 5: Expectiminimax Chapter 6: Adversarial Search Chapter 7: Evaluation function Chapter 8: Monte Carlo Tree Search Chapter 9: Negamax Chapter 10: Artificial Intelligence (II) Answering the public top questions about minimax. (III) Real world examples for the usage of minimax in many fields. (IV) 17 appendices to explain, briefly, 266 emerging technologies in each industry to have 360-degree full understanding of minimax' technologies. Who This Book Is For Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of minimax.

Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities
Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities

Author: Dumitru Motreanu

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 320

ISBN-13: 146154064X

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Boundary value problems which have variational expressions in form of inequal ities can be divided into two main classes. The class of boundary value prob lems (BVPs) leading to variational inequalities and the class of BVPs leading to hemivariational inequalities. The first class is related to convex energy functions and has being studied over the last forty years and the second class is related to nonconvex energy functions and has a shorter research "life" beginning with the works of the second author of the present book in the year 1981. Nevertheless a variety of important results have been produced within the framework of the theory of hemivariational inequalities and their numerical treatment, both in Mathematics and in Applied Sciences, especially in Engineering. It is worth noting that inequality problems, i. e. BVPs leading to variational or to hemivariational inequalities, have within a very short time had a remarkable and precipitate development in both Pure and Applied Mathematics, as well as in Mechanics and the Engineering Sciences, largely because of the possibility of applying and further developing new and efficient mathematical methods in this field, taken generally from convex and/or nonconvex Nonsmooth Analy sis. The evolution of these areas of Mathematics has facilitated the solution of many open questions in Applied Sciences generally, and also allowed the formu lation and the definitive mathematical and numerical study of new classes of interesting problems.