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| Rockafellar R.T. — Convex analysis |
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| Предметный указатель |
Norm, Euclidean 28 115 130
Norm, polar 131
Norm, polyhedral 173
Norm, Tchebycheff 36 147 173 176 215
Normal cone 15 215 222—224
Normal program 316—319
Normal vector 15 100 215
Normal vector to a hyper-plane 5
Objective function 274 295 308 314
Obverse 138
One-to-one mapping 251
Optimal solutions 274—275 295 308
Optimal value 274 295 308 315—317
Ordinary convex programs 273—91 293—294 296 298 300 320—326 429
Orientations of convex processes 416ff
Orthant, generalized 154
Orthant, non-negative 13 122 226
Orthant, positive 13
Orthogonal complement 5 121 203 336—338
Orthogonal complement, Tucker representation 9
Parallelism 4
Partial addition 20
Partial addition of epigraphs 39
Partial affine functions 70 107 431
Partial conjugacy 352
Partial derivatives 241 244 376
Partial infimal convolution 39 402
Partial quadratic functions 109 431
Penumbra 22
Perturbation function 276 280 295—306 308 314 331
Perturbations 276—277 280 294—298 301—302 311—313 316 320—326 331
Points at infinity 61
Pointwise boundedness 87
Pointwise supremum 35 78
Polar of a convex cone 121—125 146 206 219 335 426
Polar of a convex function 136—139
Polar of a convex set 124—127 136 174 426
Polar of a gauge 128—130
Polar of a norm 131 135
Polyhedral bifunctions 301—303 354
Polyhedral convex programs 301—303
Polyhedral convex sets 11 170—178 181—184 345 427
Polynomial convex functions 172—177 179—181 226 268 272
Polytope 12
Polytope, generalized 171
Positive orthant 13
Positive semi-definiteness 27
Positively homogeneous functions 30—31 66—67 114 121
Positively homogeneous functions of degree p 135
Positively homogeneous functions, generation 35 79 118 157
Products of bifunctions 409—412
Products of convex processes 422—423
Projection of a convex function 38—39 144 255—256
Projection of a convex set 19
Proper concave function 307
Proper convex bifunction 293
Proper convex function 24
Proper saddle-function 362
Proximations 339—340 431
Quadratic convex functions 27 108
Quadratic convex functions, partial 109 431
Rank 65 71 118 126
Rays 15
Recede 61 69
Recession cone 61—65 73—81 126 176 264—270 426
Recession cone of a convex function 69—70 122—123
Recession function 66—70 75—81 87
Relative boundary 44 100
Relative interior 43—50 425
Relative interior of a convex cone 50
Relative interior of an epigraph 54
| Relative interior, behavior under operations 47—50
Relative interior, characterizations 47 49 112
Relatively open sets 44 49 59 164
ri see “Relative interior”
Saddle-functions 349ff
Saddle-points 281 283 380—383 386 393 396—398
Saddle-value 379—383 386 391—393 397—398
Scalar multiplication of bifunctions 404
Scalar multiplication of convex functions 33—35 140 177 222
Scalar multiplication of convex processes 421
Scalar multiplication of convex sets 16—18 48 141 176
Scalar multiplication of saddle-functions 404
Scalar multiplication, left 33—34 140
Scalar multiplication, right 35 140
Schwarz inequality 130
Semi-continuity 51—52
Separable convex functions 270—271 285—290 337—338
Separation 95—101 175 181—183 426
Simple extensions 349 358
Simple saddle-function 368
simplex 12
Simplex algorithm 431
Simplex, generalized 154—155
Single-valued mapping 251
Smooth function 251
Strictly consistent 300—301 306 309
Strictly convex function 253—260
Strongly consistent 309
Subdifferentiability 215—217 226
Subdifferentiability of saddle-functions 393
Subdifferential 215—227 232—240 242 246
Subdifferential mappings 105 254 270—272 340 396 428
Subdifferential of a concave function 308
Subdifferential of a saddle-function 374—375 393—397
Subgradient inequality 214
Subgradients 214—227 232—240 242 246 264 270—272 298 332—333 338—341
Subgradients of concave functions 308
Subgradients of saddle-functions 374—375 393—397
Sums see “Addition”
Support functions 28 36 112—120 125 129 140 143 146 150 173 216 219 417 426—427
Support functions, effective domain 116
Support functions, level sets 118
Support of a vector 203
Supporting half-space 99
Supporting half-space , hyperplane 100
Supremum of a collection of convex functions 35 78
Symmetric convex function 110
Symmetric convex set 16
Tangent half-space 169
Tangent hyperplane 169
Tchebycheff approximation 147 176
Tchebycheff norm 173 215
Tensions 205 208 272 337—338
Totally ordered sets 232
Translate of a function 34 140
Translate of a set 4
Triangulation 84
Tucker representations 9 108 425 431
Tucker’s Complementarity Theorem 208—209
Umbra 22
Uniform boundedness 88
Uniform continuity 86—87
Uniform equicontinuity 88
Unit ba 1143
Upper closed saddle-function 365
Upper closure 359—360 368
Upper conjugate 389—391
Upper semi-continuity 51 82
Upper simple extension 349 358
Vertex 12
Vertex at infinity 154
Vertical 102
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