# Minimax and Applications

Ding-Zhu Du, Panos M. Pardalos
Springer Science & Business Media, Oct 31, 1995 - Computers - 296 pages
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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### Contents

 II 1 IV 2 VII 4 VIII 5 IX 8 X 12 XI 13 XII 15
 LXX 141 LXXII 142 LXXIII 146 LXXIV 147 LXXV 148 LXXVI 150 LXXVIII 153 LXXX 154

 XIII 17 XIV 19 XVI 25 XVIII 26 XIX 31 XX 42 XXI 51 XXII 52 XXIII 55 XXV 56 XXVI 60 XXVII 66 XXVIII 69 XXX 70 XXXI 73 XXXII 77 XXXIV 79 XXXVI 81 XXXVII 83 XXXVIII 84 XXXIX 87 XL 96 XLI 97 XLIII 98 XLIV 99 XLV 100 XLVI 103 XLVII 105 XLVIII 106 L 109 LII 110 LIII 115 LIV 117 LV 118 LVI 119 LVIII 120 LIX 122 LX 127 LXI 129 LXIII 131 LXIV 132 LXV 134 LXVI 136 LXVII 137 LXVIII 139 LXIX 140
 LXXXI 156 LXXXIII 157 LXXXV 159 LXXXVI 162 LXXXVII 167 LXXXVIII 169 LXXXIX 170 XC 173 XCII 175 XCIII 179 XCIV 188 XCV 191 XCVII 192 XCVIII 195 XCIX 203 C 217 CI 218 CII 219 CIV 221 CV 223 CVI 231 CVII 233 CVIII 238 CIX 239 CX 241 CXII 242 CXIII 244 CXIV 247 CXV 249 CXVI 250 CXVII 251 CXIX 252 CXX 253 CXXI 254 CXXII 258 CXXIII 263 CXXIV 266 CXXV 267 CXXVII 268 CXXVIII 272 CXXIX 279 CXXX 285 CXXXI 289 CXXXII 291 Copyright

### References to this book

 Deterministic Global OptimizationChristodoulos A. FloudasLimited preview - 2000
 Handbook of combinatorial optimization. 1Limited preview - 1998
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