Rockafellar R.T. — Convex analysis :: Электронная библиотека попечительского совета мехмата МГУ

Главная Ex Libris Книги Журналы Статьи Серии Каталог Wanted Загрузка ХудЛит Справка Поиск по индексам Поиск Форум

Авторизация

Поиск по указателям

Rockafellar R.T. — Convex analysis

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

Название: Convex analysis

Автор: Rockafellar R.T.

Аннотация:

R. Tyrrell Rockafellar's classic study presents readers with a coherent branch of nonlinear mathematical analysis that is especially suited to the study of optimization problems. Rockafellar's theory differs from classical analysis in that differentiability assumptions are replaced by convexity assumptions. The topics treated in this volume include: systems of inequalities, the minimum or maximum of a convex function over a convex set, Lagrange multipliers, minimax theorems and duality, as well as basic results about the structure of convex sets and the continuity and differentiability of convex functions and saddle- functions.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1970

Количество страниц: 472

Добавлена в каталог: 12.09.2007

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

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

1 2

О проекте