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| Авторизация |
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| Roberts A.W., Varberg D.E. — Convex Functions |
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| Предметный указатель |
John, F. 269 280
Jones, F. B. 225 280
Kantorovich’s inequality 208
Kaplan 256 256 280
Karlin, S., 138 153 154 176 178 249 251 253 280
Karlin’s condition 176
Kazarinoff, N. D. 189 282
Kelly, J. L. 85 280
Kemperman, J. H. B. 220 225 239 246 248 249 253 280
Kenyon, H. 224 225 281
Klee, V. L. 80 85 97 119 148 158 187 224 225 271 272 273 277 278 279 281
Kothe, G. 87 118 269 270 281
Krain — Millman theorem 85
Krasnosel’skii, M. A. 9 30 36 281
Krauss, F. 261 261 281
Kreko, B. 152 281
Kruskal, J. B. 97 281
Kuczma, M. E. 218 220 221 225 258 281
Kuhn — Tucker, conditions 174 232
Kuhn — Tucker, duality theorem 175
Kuhn, H. W. 97 174 176 178 278 281
Kurepa, S. 220 225 281
Kutateladze, S. 269 281
Landis, E. M. 28 281
Leeming, D. 282
Leipnik, R. 269 282
Level set 30 228 271
Levit’an, E. 269 282
Lidstone series 234
Limit point 40
Limits of convex functions 17 20
Lindelof property 52
linear combination 39
Linear family 249
Linear function,  -approximately 256
Linear function, characterization 214
Linear function, continuous 56
Linear function, definition of 2 55
Linear function, discontinuous 61
Linear functional, continuous 56 62
Linear functional, discontinuous 61
Linear functional, nontrivial 57
Linear functional, representation 61
Linear functional, terminology 54 55
Linear programming, canonical form 141
Linear programming, constraints 139 154
Linear programming, dual problem 147 168
Linear programming, feasible solution 140
Linear programming, objective function 139
Linear programming, optimal solution 140
Linear programming, primal problem 147
Linear programming, problem 140
Linear programming, related problem 142
Linear programming, simplex method 147 154
Linear space 41
Linearly dependent 39
Linearly independent 39 42
Lipschitz condition, definition of 4 92
Lipschitz condition, local 92
Lipschitz condition, relation to convex functions 4 7 93
Lipschitz condition, relation to finite second variation 27
Lipschitz condition, upper 96
Littlewood, J. E. 189 198 199 224 225 245 259 267 279
Locally bounded 91
Log-convex function 18 196
Lorch, E. R. 59 62 120 265 282
Lorentz, G. 185 282
Lower bounding function 223
Lowner, K. 260 261 282
Lyubich, Yu. I. 128 268 269 282
Maistrovskii, G. D. 128 268 269 282
Majorize 97
Mangasarian, O. L. 153 176 178 282
Marcus, M. 189 208 109 271 282
Marcus, S. 22 220 221 224 225 282
Martin, M. 97 281
Mathsen, R. M. 248 252 253 282
Matrix, characteristic values 69 202 208
Matrix, doubly stochastic 86 200 258
Matrix, Hadamard 271
Matrix, Hessian 103
Matrix, nonnegative definite 69 204
Matrix, payoff 129
Matrix, permutation 200
Matrix, positive definite 69 207
Matrix, symmetric 68 202 206
Matrix-convex function 259
Matrix-monotone increasing 260
Maximal element 107
Maximal monotone increasing set 32
Maximal proper subspace 57 81
Maximum of convex functions 14 124 125
Maximum of functions on  128
Maximum, global 123
Maximum, local 123
Mazur, S. 117 282
McCormick, G. P. 178 275
Mean of order t 194
Mean value theorem 71
Measure of convexity 264
Mehdi, M. R. 221 225 282
Melzak, Z. 272 282
Meschkowski, H. 272 282
Mid-convex function 211
Miles, M. J. 14 283
Mine, H. 189 208 209 271 282
Minimax theory 128
Minimum of convex functions 14 123
Minkowski’s determinant theorem 205
Minkowski’s inequality 191 193 194
Minty, G. J. 36 111 283
Mitrinovic, D. S. 189 283
Mohr, E. 221 224 225 283
Moldovan, E. 248 253 283
Mond, B. 194 278
Monotone increasing function 99
Monotone increasing set 32
Moreau, J.-J. 36 111 283
Morgenstem, O., 138 256
Motzkin, T. S. 251 252 283
Multiplicatively convex 18
n-convex function, definition of 238
n-convex function, weakly 239
n-parametcr family, definition of 246
n-parametcr family, unrestricted 252
n-simplex 77
Naimark, M. A. 52 54 283
Namioka, I. 85 280
Nashed, M. Z. 117 283
Natanson, I. P. 7 9 10 23 27 116 119 222 229 265 283
Nearest points 14 187 271
Nested set property 52
Nevanlinna, F. 71 283
Nevanlinna, R. 71 283
Nishiura, T. 96 283
Nonnegative orthant 140
Norm of a linear transformation 59 61
Norm, equivalence 47
Norm, Euclidean 39
Norm, examples of 45 46 198
Norm, general notion of 44
Norm, p-norms 198
Norm, smooth 118
Norm, uniformly smooth 118
Normed linear space 44
Normed linear space, smooth 118
Normed linear space, uniformly smooth 118
Nullspacc 57
Oberg, R. 269 282
Objective function 139
| Olmsted, J. M. H. 266 278
Open cover 40
Open set 40 47
Opial, Z. 252 253 283
Oppenheim’s inequality 208
Ore, O. 271 283
Orlicz, W. 36 274
Orthogonal vectors 41
Ostrow, K. 22 276
Ostrowski, A. 219 220 224 225 259 259 283
Owen, G. 138 283
Parallelogram law 53
Partially monotone function 218
Partially ordered 107
Payoff matrix 129
Peixoto, M. M. 9 243 245. 283 284
Permutation matrix 200
Perturbation function, 178
Peterson, E. L. 128 277
Phelphs, R. R. 118 284
Pierskalla, W. P. 227 231 233 278
Pivoting 156
Point (vector) 38 41
Polya, G., 189 198 199 224 225 233 235 236 245 259 267. 279 284
Polyhedral 125 127
Polytopc 77 127
Polzak, B. 268 269 282 284
Ponstein, J. 104 231 233 284
Popoviciu, T. 9 28 237 238. 246 252 284
Pre-Hilbert space 50
Primal problem, convex programming 174
Primal problem, linear programming 147
Protter, M. H. 235 237 284
Pseudo-convex function, 104
Quadratic programming 177
Quasi-convex function 104 228
Quintas, L. 266 284
Rademacher, H. 119 284
Rado, T. 15 254 255 284
Randolph, J. F. 9 284
Real inner product space 50
Real linear space 41
Reid, W. 245 246 284
Relative interior 78 80
Relatively open 79
Restrepo, G. 270 284
Rice, J. R. 185. 284
Riesz, F. 14 28 254 255 284
Riesz’s convexity theorem 266
Riesz’s lemma 52
Roberts, A. W. 28 271 285
Rockafellar, R. T. 21 36 94 96 110 111 112 118 123 127 148 152 162 170 178 267 275 285
Rogers, C. A. 271 285
Rotundity 118 270
Roydon, H. L. 52 54 285
Rubin, H. 267 285
Rubinov, A. 269 281
Rudin, W. 187 265 285
Russell, A. M. 28 266 285
Rutickii, Y. B. 9 30 36 281
Saaty, T. L. 271 285
Saddlepoint 131
Salem, R 267 285
Samuelson, P. A. 154 277
Sansone, G. 256 256 285
Scalar multiplication 39
Schnitzer, F. 96 283
Schur, I. 258 259 259 285
Schur-convex function 209 258
Schwartz, J. T. 62 277
Secbach, J. 266 286
Semi-continuous function, lower 112
Semi-continuous function, upper 96
Sengenhorst, P. 9 285
Separation of convex sets, definition of 81
Separation of convex sets, nice 85
Separation of convex sets, proper 85
Separation of convex sets, strict 85
Separation of convex sets, strong 81
Separation of convex sets, theorems 81 83 85
Sequences of convex functions 17 20
Sequentially compact 52
Sharma, A. 282
Sherman, S. 261 262 274
Shisha, O. 269 285
Sierpinski, W. 221 225 285
Simmons, C. L. 28 276
Simonnard, M. 152 154 285
Simplex method 147 158
Sion, M. 138 285
Slack variables 142
Slater’s condition 176
Smajdor, A. 22 286
Smulian, V. L. 118 270 286
Solovv, R. M. 154 277
Solution, feasible 140 171
Solution, optimal 140
Solution, strictly feasible 172
Solution, unbounded 151
Spectrum 259
Sphere packing 271
Starlike function 256
Steen, L. 266 286
Steinberg, D. 154 276
Stoer, J. 120 178 286
Stolz, O. 8 286
Strategies, mixed 134
Strategies, optimal 134
Strategies, pure 134
Strictly convex function, characterizations 9 10 98 99
Strictly convex function, definition of 2
Strictly convex space 184
Strictly monotone increasing 99
Stromberg, K. 30 194 199 266 279
Strongly convex function 268
Studden, W. J. 249 251 253 280
Subdifferential 32 110
Subharmonic function,  -approximately 257
Subharmonic function, definition of 254
Subharmonic function, pluri 255
subspace 44 53
Sum of order t 196
Sundaresan, K. 119 270 286
Supnick, F. 266 284
Support function for a convex set 95
Support of convex functions at boundary points 14
Support of convex functions, continuous 108
Support of convex functions, definition of 12 108
Support of convex functions, line of support 12
Support of convex functions, uniqueness 12 110 113 115
Support of convex sets 84 112
Suprema of convex functions 16 30
Supremum 40
Symmetric bilinear form 68 69
Symmetric function 258
Symmetric matrix 68 202 206
Sz.-Nagy, B. 14 28 284
Szekeres, G. 22 286
Tableau 155
Taylor, A. E. 52 53 54 62 107 216 217 267 286
Taylor’s Theorem 70 119
Tchebycheff system 250
Thielman, H. P. 269 286
Thompson, R. G. 104 275
Thorin, G. 267 286
Tikhomirov, V. 36 111 280
Titchmarsh, E. 267 286
Topologically equivalent norms 47 199
Topologically isomorphic spaces 50
Tornheim, L. 246 249 251 252 286
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