Minimax and Applications

Minimax and Applications

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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.
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Product details

  • Hardback | 296 pages
  • 162.56 x 233.68 x 25.4mm | 589.67g
  • Dordrecht, Netherlands
  • English
  • 1995 ed.
  • XIV, 296 p.
  • 0792336151
  • 9780792336150

Table of contents

Preface. Minimax theorems and their proofs; S. Simons. A survey on minimax trees and associated algorithms; C.G. Diderich, M. Gengler. An iterative method for the minimax problem; L. Qi, W. Sun. A dual and interior point approach to solve convex min-max problems; J.F. Sturm, S. Zhang. Determining the performance ratio of algorithm MULTIFIT for scheduling; F. Cao. A study of on-line scheduling two-stage shops; B. Chen, G.J. Woeginger. Maximin formulation of the apportionment of seats to parliament; T. Helgason, et al. On shortest k-edge connected Steiner networks with rectilinear distance; D.F. Hsu, et al. Mutually repellant sampling; S.-H. Teng. Geometry and local optimality conditions for bilevel programs with quadratic strictly convex lower levels; L.N. Vicente, P.H. Calamai. On the spherical one-center problem; G. Xue, S. Sun. On min-max optimization of a collection of classical discrete optimization problems; G. Xu, P. Kouvelis. Heilbronn problem for six points in a planar convex body; A.W.M. Dress, et al. Heilbronn problem for seven points in a planar convex body; L. Yang, Z. Zeng. On the complexity of min-max optimization problems and their approximation; K.-I Ko, C.L. Lin. A competitive algorithm for the counterfeit coin problem; X.-D. Hu, F.K. Hwang. A minimax alphabeta relaxation for global optimization; J. Gu. Minimax problems in combinatorial optimization; F. Cao, et al. Author index.
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Review quote

` ... a valuable book carefully written in a clear and concise fashion. The survey papers give coherent and inspiring accounts ... coverage of algorithmic and applied topics ... is impressive. Both graduate students and researchers in fields such as optimization, computer science, production management, operations research and related areas will find this book to be an excellent source for learning about both classic and more recent developments in minimax and its applications. The editors are to be commended for their work in gathering these papers together.'
Journal of Global Optimization, 11 (1997)
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