Minimax and applications
著者
書誌事項
Minimax and applications
（Nonconvex optimization and its applications, v. 4）
Kluwer Academic Publishers, c1995
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注記
Series number from series list at end; incorrect number on p. facing t.p.: 5
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
- 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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