Minimax Theory And Applications
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Minimax And Applications
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Author : Ding-Zhu Du
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-10-31
Minimax And Applications written by Ding-Zhu Du and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-10-31 with Computers categories.
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 And Applications
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Author : Ding-Zhu Du
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Minimax And Applications written by Ding-Zhu Du and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Computers categories.
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
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Author : Biagio Ricceri
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Minimax Theory And Applications written by Biagio Ricceri and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
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 Methods In Critical Point Theory With Applications To Differential Equations
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Author : Paul H. Rabinowitz
language : en
Publisher: American Mathematical Soc.
Release Date : 1986-07-01
Minimax Methods In Critical Point Theory With Applications To Differential Equations written by Paul H. Rabinowitz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-07-01 with Mathematics categories.
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.
Minimax Theorems
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Author : Michel Willem
language : en
Publisher: Birkhäuser
Release Date : 1997-02-01
Minimax Theorems written by Michel Willem and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-02-01 with Mathematics categories.
A textbook for an advanced graduate course in partial differential equations. Presents basic minimax theorems starting from a quantitative deformation lemma; and demonstrates their applications to partial differential equations, particularly in problems dealing with a lack of compactness. Includes some previously unpublished results such as a treatment of the generalized Kadomtsev-Petviashvili equation. Annotation copyright by Book News, Inc., Portland, OR
Morse Theory Minimax Theory And Their Applications To Nonlinear Differential Equations
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Author : Haim Brézis
language : en
Publisher:
Release Date : 2003
Morse Theory Minimax Theory And Their Applications To Nonlinear Differential Equations written by Haim Brézis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Chebyshev approximation categories.
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.
Kkm Theory And Applications In Nonlinear Analysis
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Author : George Xian-Zhi Yuan
language : en
Publisher: CRC Press
Release Date : 1999-02-09
Kkm Theory And Applications In Nonlinear Analysis written by George Xian-Zhi Yuan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-02-09 with Mathematics categories.
This reference provides a lucid introduction to the principles and applications of Knaster-Kuratowski-Mazurkiewicz (KKM) theory and explores related topics in nonlinear set-valued analysis.
Critical Point Theory And Its Applications
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Author : Wenming Zou
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-10
Critical Point Theory And Its Applications written by Wenming Zou and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-10 with Mathematics categories.
This book presents some of the latest research in critical point theory, describing methods and presenting the newest applications. Coverage includes extrema, even valued functionals, weak and double linking, sign changing solutions, Morse inequalities, and cohomology groups. Applications described include Hamiltonian systems, Schrödinger equations and systems, jumping nonlinearities, elliptic equations and systems, superlinear problems and beam equations.
Mathematical Statistics
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Author : Aleksandr Petrovich Korostelev
language : en
Publisher: American Mathematical Soc.
Release Date :
Mathematical Statistics written by Aleksandr Petrovich Korostelev and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
"This book is designed to bridge the gap between traditional textbooks in statistics and more advanced books that include the sophisticated nonparametric techniques. It covers topics in parametric and nonparametric large-sample estimation theory. The exposition is based on a collection of relatively simple statistical models. It gives a thorough mathematical analysis for each of them with all the rigorous proofs and explanations. The book also includes a number of helpful exercises."--Publisher's description.
Fixed Point Theory And Applications
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Author : Yeol Je Cho
language : en
Publisher: Nova Publishers
Release Date : 2002
Fixed Point Theory And Applications written by Yeol Je Cho and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
Fixed Point Theory & Applications Volume II