|
|
 |
| Àâòîðèçàöèÿ |
|
|
|
| Ïîèñê ïî óêàçàòåëÿì |
|
|
|
|
|
|
|
 |
|
|
|
| Rockafellar R.T. — Convex analysis |
|
|
|
| Ïðåäìåòíûé óêàçàòåëü |
Abnormal program 318
Addition of convex cones 22
Addition of convex functions 33 77 145 176 179—180 223 263
Addition of convex processes 415 421
Addition of convex sets 16—17 49 74—75 146 175 183
Addition of epigraphs 34
Addition of saddle-functions 402
Adjoint of a bifunction 309—326 330 353—358 401—412
Adjoint of a convex process 417ff
Adjoint of a linear transformation 3 9 310
aff see “Affine hull”
Affine functions 23 25 27 102—103
Affine functions, partial 70 107 431
Affine hull 6 45 154
Affine hull of convex cone 15
Affine hull, characterization 113
Affine independence 6—7 154
Affine sets 3—9
Affine sets, closed halves 165—166
Affine sets, representation 4—8
Affine transformations 7—8 44—45
Alternative system of inequalities 201
Asymptotic cone 61
Ball 43
Barrier cone 15 113 123
Barycenter 12
Barycentric coordinates 7
Bi-affine functions 302
Bifunction 291ff (see also “Convex bi-functions”)
Bilinear functions 351—352 411
Boundedness conditions 54 64 68—69 88 123
Caratheodory’s theorem 153—157 427
Chemical equilibrium problem 430
Circulations 204 208 272 337—338
Cl see “Closure”
Closed bifunction 293
Closed concave function 308
Closed convex function 52 (see also “Closure”)
Closed saddle-function 363 (see also “Closure”)
Closure of a bifunction 293 305—306 310 403 407
Closure of a concave function 307—308
Closure of a convex function 51—59 72—81 102—104 218—219 425
Closure of a convex process 415
Closure of a convex set 43—50 72—81 112 421—422
Closure of a saddle-function 359—369 390
Closure of an epigraph 52
Co-finite 116 259—260 411—412
Complete non-decreasing curves 232 338 428
Composition of a convex function and a linear transformation 38 78
Composition of convex functions 32
Composition of convex processes 416 422—423
Concave bifunctions 308ff
Concave closure of a saddle-function 350—353
Concave functions 25 307—308 426
Concave functions, monotone conjugates 110
Concave programs 308ff
Concave-convex functions 349ff
Cone 13
Conjugacy correspondence 104 123—124
Conjugacy correspondence for saddle-functions 389ff
Conjugate concave functions 111 308
Conjugate convex functions 104—111 113—118 121—124 133—137 140—150 173 179—180 263—264 405 421 425—426
Conjugate convex functions, definition 104
Conjugate convex functions, subgradients 218
Conjugate saddle-functions 390—391 395 432
Consequence 199
Consistency 185 295 309 315
Constancy space 69
Continuity of convex functions 82—89 426
Continuity of derivatives 227—238
Continuity of gradient mappings 246 376—377
Continuity of saddle-functions 370—371
Continuity, joint 89
Continuity, uniform 86—87
Continuous extensions 85
conv see “Convex hull”
Convergence of convex functions 90—91 426
Convergence of gradients 248—249
Convergence of saddle-functions 372 375—378
Convergence of subgradients 233—236
Convex bifunctions 293—306 309—311 350—358 384—389 401—412 417—418
Convex closure of a saddle-function 350—353
Convex combinations 11—12
Convex combinations of points and directions 154
Convex cones 13—15 22 50
Convex cones, generation 78 122 126 156 178
Convex cones, polar 121—125
Convex cones, polyhedral 170 178
Convex cones, separation 100—101
Convex function 23
Convex function, co-finite 259
Convex function, differential conditions for convexity 26—27
Convex function, finitely generated 172—173
Convex function, interpolation properties 25
Convex function, Legendre type 258
Convex function, partial quadratic 109 431
Convex function, polyhedral 172—177
Convex function, polynomial 268
Convex function, quadratic 27 108
Convex function, separable 270—271 285—290 337—338
Convex function, symmetric 109—110
Convex hull 12 177 427
Convex hull of a set of points and directions 153—155
Convex hull, of a bounded set 158
Convex hull, of a collection of convex functions 37 81 149 156
Convex hull, of a collection of convex sets 18 80 156—157
Convex hull, of a non-convex function 36 103 157—158
Convex hull, of two convex cones 22
Convex hull, relative interior 50
Convex processes 413—423 432
Convex processes, polyhedral 415
Convex programs, generalized 291—326 355—356 385—387
Convex programs, normal 316—319
Convex programs, ordinary 273—291 293—294 296 298 300 320—326 429
Convex programs, polyhedral 301—303
Convex set 10
Convex set as a cross-section of a cone 15
Convex set, finitely generated 170—171
Convex set, polyhedral 11
Convex set, symmetric 16
Convex-concave functions 349ff
Cyclically monotone mappings 238—240
Decomposition principle 285—290 312—313 429
Derivatives, directional 213—221 226 244—245 264 299—301 372—377
Derivatives, partial 241 244 376
Derivatives, right and left 214 216 227—232
Differentiability 241—246 428
Differentiability of saddle-functions 375—376
DIM see “Dimension”
Dimension of a convex function 23 71
Dimension of a convex set 12—13 45—46 126
Dimension of an affine set 4
Direct sums 19 49
Directed graphs 204 208 272 337—338
Direction 60
Direction of affinity 70
Direction of constancy 69
Direction of linearity 65
Direction of recession 61 69 264—270
Directional derivatives 213—221 226 244—245 264 299—301 372—377
Distance function 28 34
Distributive inequalities 416
DOM see “Effective domain”
Dual programs 310—338 355—356 429ff
Dual systems of inequalities 201
Effective domain of a bifunction 293
Effective domain of a concave function 307
Effective domain of a convex function 23 25 122
Effective domain of a convex process 413
Effective domain of a saddle-function 362 366 391—392
| Effective domain, relative interior 54
Eigensets 423
Elementary vectors 203—208 272 428
Epi see “Epigraph”
Epigraph 23 307
Epigraph, closure 52
Epigraph, relative interior 54
Epigraph, support function of 119
Equi-Lipschitzian 87—88
Equicontinuity 88
Equilibrium prices 276—277 280 299—300
Equivalent saddle-functions 363—369 383 394
Essentially smooth function 251—258
Essentially strictly convex function 253—260
Euclidean metric 43
Exposed directions 163 168
Exposed faces 162—163
Exposed points 162—163 167—168 243 427
Exposed rays 163 169
Extensions of saddle-functions 349 358 363 366 369
Extreme directions 162—166 172
Extreme points 162—167 172 344—345 427
Extreme points at infinity 162
Extreme rays 162 167
Faces 162—165 171 427
Faces, exposed 162—163
Farkas’ lemma 200—201
Feasible solutions 274 295 308 315
Fenchel’s Duality Theorem 327ft 408 430
Fenchel’s inequality 105 218
Finitely generated convex function 172—173
Finitely generated convex set 170—171
Flat 3
flows 204 208 272 337—338
Fully closed saddle-function 356 365
Gale — Kuhn — Tucker Theorem 317 337 421 430—431
Gauge 28 35 79 124—125 128—131 427
Gauge-like functions 133
Generalized convex programs 291—326 355—356 385—387
Generalized polytope 171
Generalized simplex 154—155
Generators 170
Geometric mean 27 29
Geometric programming 324—326 430
Gradients 213 241—250 300 375—378 396
Graph domain 293
Graph function 292
Half-spaces 10 99 112 160
Half-spaces in  102
Half-spaces, homogeneous 101
Half-spaces, tangent 169
Half-spaces, upper 102
Half-spaces, vertical 102
Helly’s theorem 191—197 206 267 427—428
Hessian matrix 27
Hyperplanes 5
Hyperplanes, in 102
Hyperplanes, representation 5
Hyperplanes, supporting 100
Hyperplanes, tangent 169
Hyperplanes, vertical 102
Image of a convex function 38 75 142 175 255 405 409—412 416 421
Image of a convex set 19 48 73 143 174 414—415 421—422
Image-closed bifunction 352—353
Improper convex function 24 34 52—53
Improper saddle-function 366
Incidence matrix 204 208
Inconsistency 185 315
Indicator bifunction 292—293 310 355 417
Indicator function 28 33 425
Indicator function, conjugate 113—114
Inequalities 129—130 425 428
Inequalities, between functions 38 104
Inequalities, between vectors 13
Inequalities, consistent 185
Inequalities, convex 29 55 58 185—197
Inequalities, homogeneous 14
Inequalities, linear 10—11 13—14 62 65 113 122 170 185 198—209
Infimal convolution 34 38 76—77 145 175 179—181 254 425 427
Infimal convolution of bi-functions 401—404
Infimal convolution, partial 39
Inner product equation 355 409—412 419—421
Inner product of a vector and a function 350
Inner product of a vector and a set 417
Inner product of two functions 408—412
Inner product of two sets 422—423
Inner product of two vectors 3
int see “Interior”
Interior 43—44 47 112
Intersections of convex cones 13 22
Intersections of convex sets 10 64 145
Intersections, relative interiors 47
interval 202
Inverse addition 21
Inverse addition of epigraphs 40
Inverse bifunction 384—385 388—389 401 405—406
Inverse image of a convex function 38 78 141 225
Inverse image of a convex set 19 49 64 143 174
Inverse process 414 418
Kernel of a saddle-function 367—369
Kuhn — Tucker coefficients 274—277 280 429
Kuhn — Tucker conditions 282—284 304 333—338 386—387 429
Kuhn — Tucker theorem 283 387
Kuhn — Tucker vectors 274—290 295—306 309 387
Lagrange multipliers 273—274 280 283 429
Lagrangian function 280—290 296—298 302—305 309 314 385—387
Lattice of convex functions 38
Lattice of convex processes 416
Lattice of convex sets 18
Legendre conjugate 256—260
Legendre transformation 251 256 427 429
Level sets 28—29 55 58—59 70 123 127 222 263—265
Level sets of support functions 118
Line 3—4
Line segment 10 12
Lineality 65 126
Lineality of a convex function 70 117
Lineality space 65 70 117 126
Linear combinations, convex 11
Linear combinations, of convex functions 33;
Linear combinations, of convex sets 17—18
Linear combinations, positive and non-negative 14
Linear programs 301—302 311—312 317 332 334—335 337 425
Linear variety 3
Lipschitz conditions 116 237 370—371
Lipschitzian 86
Locally simplicial sets 84—85 184
Lower boundary 33
Lower closed saddle-function 365
Lower closure 357—359 368
Lower conjugate 389—391
Lower semi-continuity 51—52 72 77
Lower semi-continuous hu 1152 54
Lower simple extension 349 358
Maximum of a convex function 342—346
minimax 379 391—393 397—398 431
Minimum set 263—266
Minimum set of a convex function 263ff
Minkowski metric 132
Monotone conjugacy 111 426
Monotone mappings 240 340 396
Monotonicity 68—69 77 85—86
Moreau’s Theorem 338
Multiplication of bifunctions 409—412
Multiplication of convex processes 422—423
Network programming 272 337—338 431
Non-decreasing curves 232 338
Non-decreasing functions 68—69 77 85—86 232 338
Non-negative orthant 13 122 226
Norm 129—132 136 427
|
|
|
| Ðåêëàìà |
|
|
|
|
|
Î ïðîåêòå