Minimax and Applications

Minimax and Applications
Author: Ding-Zhu Du
Publisher: Springer Science & Business Media
Total Pages: 300
Release: 2013-12-01
Genre: Computers
ISBN: 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
Total Pages: 278
Release: 2013-06-29
Genre: Mathematics
ISBN: 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.

Introduction to Minimax

Introduction to Minimax
Author: V. F. Dem’yanov
Publisher: Courier Corporation
Total Pages: 324
Release: 2014-03-05
Genre: Mathematics
ISBN: 0486793281

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Geared toward students of mathematical programming, this user-friendly text offers a thorough introduction to the part of optimization theory that lies between approximation theory and mathematical programming. 37 illustrations. 1974 edition.

Minimax and Monotonicity

Minimax and Monotonicity
Author: Stephen Simons
Publisher: Springer
Total Pages: 173
Release: 2006-11-14
Genre: Mathematics
ISBN: 3540689311

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Focussing on the theory (both classical and recent) of monotone multifunctions on a (possibly nonreflexive) Banach space, this book looks at the big convexification of a multifunction; convex functions associated with a multifunction; minimax theorems as a tool in functional analysis and convex analysis. It includes new results on the existence of continuous linear functionals; the conjugates, biconjugates and subdifferentials of convex lower semicontinuous functions, Fenchel duality; (possibly unbounded) positive linear operators from a Banach space into its dual; the sum of maximal monotone operators, and a list of open problems. The reader is expected to know basic functional analysis and calculus of variations, including the Bahn-Banach theorem, Banach-Alaoglu theorem, Ekeland's variational principle.

Minimax Detection Station Placement

Minimax Detection Station Placement
Author: Richard D. Smallwood
Publisher:
Total Pages: 28
Release: 1965
Genre: Mathematical optimization
ISBN:

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Minimax Theorems

Minimax Theorems
Author: Michel Willem
Publisher: Springer Science & Business Media
Total Pages: 168
Release: 2012-12-06
Genre: Mathematics
ISBN: 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 Under Transportation Constrains

Minimax Under Transportation Constrains
Author: Vladimir Tsurkov
Publisher: Springer Science & Business Media
Total Pages: 324
Release: 1999-04-30
Genre: Mathematics
ISBN: 9780792356097

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Transportation problems belong to the domains mathematical program ming and operations research. Transportation models are widely applied in various fields. Numerous concrete problems (for example, assignment and distribution problems, maximum-flow problem, etc. ) are formulated as trans portation problems. Some efficient methods have been developed for solving transportation problems of various types. This monograph is devoted to transportation problems with minimax cri teria. The classical (linear) transportation problem was posed several decades ago. In this problem, supply and demand points are given, and it is required to minimize the transportation cost. This statement paved the way for numerous extensions and generalizations. In contrast to the original statement of the problem, we consider a min imax rather than a minimum criterion. In particular, a matrix with the minimal largest element is sought in the class of nonnegative matrices with given sums of row and column elements. In this case, the idea behind the minimax criterion can be interpreted as follows. Suppose that the shipment time from a supply point to a demand point is proportional to the amount to be shipped. Then, the minimax is the minimal time required to transport the total amount. It is a common situation that the decision maker does not know the tariff coefficients. In other situations, they do not have any meaning at all, and neither do nonlinear tariff objective functions. In such cases, the minimax interpretation leads to an effective solution.

Minimax Algebra

Minimax Algebra
Author: R. A. Cuninghame-Green
Publisher: Springer Science & Business Media
Total Pages: 273
Release: 2012-12-06
Genre: Business & Economics
ISBN: 3642487084

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A number of different problems of interest to the operational researcher and the mathematical economist - for example, certain problems of optimization on graphs and networks, of machine-scheduling, of convex analysis and of approx imation theory - can be formulated in a convenient way using the algebraic structure (R,$,@) where we may think of R as the (extended) real-number system with the binary combining operations x$y, x®y defined to be max(x,y),(x+y) respectively. The use of this algebraic structure gives these problems the character of problems of linear algebra, or linear operator theory. This fact hB.s been independently discovered by a number of people working in various fields and in different notations, and the starting-point for the present Lecture Notes was the writer's persuasion that the time had arrived to present a unified account of the algebra of linear transformations of spaces of n-tuples over (R,$,®),to demonstrate its relevance to operational research and to give solutions to the standard linear-algebraic problems which arise - e.g. the solution of linear equations exactly or approximately, the eigenvector eigenvalue problem andso on.Some of this material contains results of hitherto unpublished research carried out by the writer during the years 1970-1977.

Graham Kerr's Minimax Cookbook

Graham Kerr's Minimax Cookbook
Author: Graham Kerr
Publisher: Broadway
Total Pages: 247
Release: 1992
Genre: Cooking
ISBN: 9780385424882

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The TV chef presents 150 original recipes and discusses strained yogurt, pressure cooking, and more

H∞-Optimal Control and Related Minimax Design Problems

H∞-Optimal Control and Related Minimax Design Problems
Author: Tamer Başar
Publisher: Springer Science & Business Media
Total Pages: 417
Release: 2009-05-21
Genre: Science
ISBN: 0817647570

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This book is devoted to one of the fastest developing fields in modern control theory - the so-called H-infinity optimal control theory. The book can be used for a second or third year graduate level course in the subject, and researchers working in the area will find the book useful as a standard reference. Based mostly on recent work of the authors, the book is written on a good mathematical level. Many results in it are original, interesting, and inspirational. The topic is central to modern control and hence this definitive book is highly recommended to anyone who wishes to catch up with important theoretical developments in applied mathematics and control.