Roberts A.W., Varberg D.E. — Convex Functions :: Электронная библиотека попечительского совета мехмата МГУ

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Roberts A.W., Varberg D.E. — Convex Functions

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Название: Convex Functions

Авторы: Roberts A.W., Varberg D.E.

Язык:

Рубрика: Математика/Анализ/Продвинутый анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1973

Количество страниц: 300

Добавлена в каталог: 02.04.2005

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Предметный указатель

$\lambda(n)$ -convex function      252
$\lambda(n)$ -family      251
$\mathcal{F}$ -convex      241
$\mathcal{F}$ -mid-convex      241
$\mathcal{F}_n$ -convex, definition of      247
$\mathcal{F}_n$ -convex, weakly      247
$\mathcal{F}_n\mathcal{L}$ -convex      243
$\mathcal{G}$ -convex function      269
$\varepsilon$ -neighborhood      40 46
Absolute continuity      4 96
Absolutely monotonic function      234
Aczel, J.      217 269 273
Additive function      217
Affine combination      75
Affine function (transformation), characterizations      7 55 214
Affine function (transformation), definition of      2 55
Affine hull      75
Affine set, characterizations      74 75 79
Affine set, closure properties      75
Affine set, definition of      73
Aggeri, J. C      97 273
Alexandroff, A. D.      28 120 273
Almost convex function      257
Anderson, B. J.      21 273
Anderson, R. D.      119 273
Approximately convex function      256
Approximation of convex functions      269
Approximation problem      181
Arsove, M. G.      28 273
Artin, E.      8 9 21 216 222 224 273
Ascoli, G      117 274
Asplund, E.      96 118 274
Banach space      47
Banach, S.      62 274
Bary, N. K.      265 274
Barycentric coordinates      77
Basis, definition of      39 42
Basis, Hamel      217
Basis, orthonormal      53
Basis, standard      39
Beale, E. M. L.      147 154 274
Beckenbach, E. F., P      15 20 189 193 207 208 209 240 242 244 245 246 255 255 258 259 274
Bellman, R.      189 193 207 208 209 255 255 258 259 274
Bendat, J.      261 262 274
Bereanu, B.      218 274
Berge, C      36 138 152 176 178 274
Bergstrom’s inequality      209
Bernstein, B.      103 274
Bernstein, F.      218 220 223 224 274
Bernstein, S.      233 274
Besicovitch, A. S.      22 274
Best approximation      181
Bilinear transformation      68
Bing, R. H.      242 246
Birkoff, G.      200 274
Birnbaum, Z.      36 274
Blackwell, D.      138 275
Blumberg, H.      221 225 275
Boas, R. P.      234 235 236 236 237 239 240 275
Boltyanskii, V. G.      73 271 287
Bolzano — Weierstrass theorem      40 52
Bonnesen, T.      73 275
Bonsall, E. F.      243 246 275
Borel, E.      138 275
Borsuk’s covering problem      271
Boundary behavior of closed convex functions      30 95
Boundary behavior of convex functions, continuity      4
Boundary behavior of convex functions, derivatives      6
Boundary behavior of convex functions, envelope function      97
Boundary behavior of convex functions, maximum      127
Boundary point      40 47 84
Bounded function      3
Bounded linear transformation      56 61
Bounded set      40 47
Boundedly polyhedral      96
Bourbaki, N.      219 225 275
Bracken, J.      178 275
Bremermann, H. J.      255 255 267 269 275
Brendsted, A.      36 97 111 187 271 275 275
Brenner, J.      271 275
Brock, W. A.      104 275
Bruckner, A. M.      22 276
Brunn — Minkowski function      267
Brunn, H.      8 276
Buck, R. C      41 47 54 66 104 120 128 185 187 223 276
Bulanov, A. P.      269 276
Bullen, P. S.      194 200 238 240 248 276
Busemann, H.      120 265 276
Carafheodory’s theorem      76
Cauchy sequence      41
CBS inequality      41 53 191
Cebaevskaja, I. V.      253 276
Chain      107
Chain rule      66
Charnes, A.      154 160 276
Chaundy, T. W.      104 276
Chebyshev set      187
Cheney, E. W.      185 186 187 276
Ciesielski, Z.      239 240 276
Clement, P. A.      245 246 276
Close to convex      256
Closed convex function      30 95 111
Closed set      40 47 51
Closure of a set      40 51
Closure properties, convex functions on $\mathbb{L}$       94
Closure properties, convex functions on $\mathbb{R}$       13
Colonel Blotto game      137
Combination, affine      75
Combination, convex      75
Combination, general      217
Combination, infinite convex      267
Combination, linear      39
Combination, rational convex      212
Compact set      40 47
Complete normed linear space      47
Completely convex function, almost      236
Completely convex function, definition of      235
Completely convex function, minimal      235
Completely monotonic      234
Complex convexity      255
Composition of convex functions,      16 20
Concave function      2
Conjugate convex function, closed      30
Conjugate convex function, definition of      21 30 110
Conjugate convex function, properties      28 111
Conjugate convex function, relation to convex programming      178
Continuous function      54
Continuously differentiable      68
Converge      40 47
Convex combination      75
Convex function, absolute continuity      4 9
Convex function, boundedness      3
Convex function, characterizations      8 9 97
Convex function, closed      30 95 111
Convex function, conjugate      21 28 30 110
Convex function, continuity      4 7 91 215
Convex function, definition of      2 89
Convex function, derivatives      5 10 11 97
Convex function, differentiability      7 101 113
Convex function, Lipschitz condition      4 7 93
Convex function, maxima-minima      14 122
Convex function, support      12 104
Convex programming      170
Convex sequences      265
Convex set, characterization      75
Convex set, closure properties      75 79
Convex set, definition of      73
Convex set, separation      81 83
Convex set, support      84
Convex set, topological properties      77

Convex, hull      75
Convexity at a point      268
Cooper, L.      154 276
Cooper, W. W.      154 160 276
Core      80
Counterexamples      266
Crownovcr, R. M.      28 276
Csaszar, A.      221 225 276
Cudia, D. F.      118 270 277
Cummings, I..      271 275
Curtis, Jr., P. C      251 253 277
Cycling      160
Dantzig, G. B.      153 277
Danzer, L.      80 277
Davies, R. O.      22 274
Davis, C      260 261 262 277
Day, M. M.      42 53 54 270 277
Daykin, D. E.      194 277
de Finetti, B.      228 229 233 277
de la Vallee Poussin, C      28 277
Deak, E.      221 225 277
Debrunner, H.      271 272 279
Derivative, directional      62
Derivative, distribution      265
Derivative, Frechet      63 114
Derivative, Gateau differential      113
Derivative, generalized      32
Derivative, generalized second      14
Derivative, gradient      101
Derivative, one-sided      5
Derivative, partial      63
Derivative, Schwarz      265
Derivative, second Frechet      67 119
Dieudonne, J.      70 71 118 270 277
Differences of convex functions      22
Differential inequality      245
Dimension of a convex set      76 80
Dimension of a linear space      42
Dines, L. L.      112 277
Distance function      95
Divided differences      24 237 260 265 266
Doetsch, G.      218 220 223 224 274
Dorfman, R.      154 277
Doubly stochastic matrices      86 200 258
Dresner, M.      137 138 277
Dual problem, convex programming      175
Dual problem, linear programming      147 168
Duality theorem of Linear Programming      148
Duality, conjugate convex functions      29 178
Duality, convex programs      174
Duality, general notion      28
Duality, linear programs      147
Duality, linear spaces      60
Duality, set operations      52
Duffin, R. J.      128 277
Dunford, N.      62 277
Eggleston, H. G.      73 80 277
Eliezer, C. J.      194 277 278
Envelope      97 112
Epigraph      80 95
Euclidean n-space $\mathbb{R}^n$       38
Evelyn, C. J. A.      104 276
Expected payoff function      134
Exposed point      86
Exterior point      40 47
Extreme point      84 86 145 200 208 269
Extreme subset      86
Fan, K.      138 278
Farkas, J.      152 278
Farkas’ lemma      152
Feasible set      140 171 175
Feller, W.      120 276
Fenchel, W.      9 36 73 96 110 111 228 229 233 271 272 27:5 278
Finite dimensional space      42
Flat      73
Ford, L. R.      154 278
Forsythe, G.      267 278
Four color problem      271
French railroad space      266
Friedman, B.      96 27S
Fulkerson, D. R.      154 278
Functional equations      269
Functions      see “Affine function Convex etc.”
Functions, terminology      54
Gale, D.      97 148 154 275
Games      128
Gamma function      21
Gateaux differential, definition of      113
Gateaux differential, relation to Frechet derivative,      114 11
Gateaux differential, strong      117
Gauge function      95 216
Gelbaum, B.      266 278
Generalized convex functions      240
Geometric mean-arithmetic mean, condition for equality      192
Geometric mean-arithmetic mean, generalized inequality      195
Geometric mean-arithmetic mean, inequality      190
Geometric programming,      128
Ger, R.      221 225 239 240 278
Gerretsen, J.      256 256 285
Ghouila — Houri, A.      36 138 152 176 178 274
Girshick, M. A.      138 275
Gradient      101
Green, J. W.      9 243 244 246 257 257 278
Greenbcrg, H. J.      227 231 233 278
Grunbaum, B.      73 80 267 271 272 277 278 279
Guberman, I. Ja.      94 279
Hadamard matrices      271
Hadamard, J.      8 279
Hadamard’s determinant theorem      205
Hadamard’s three circles theorem      267
Hadley, G.      154 118 279
Hadwiger, H.      271 272 279
Hahn — Banach theorem,      105
Halfspace      81
Halmos, P.      42 69 260 279
Halperin      1 265 279
Hamel, G.      217 279
Hammer, P.      266 279
Hanai, S.      245 246 279
Hardy, G. H.      9 189 198 199 224 225 245 259 267 279
Harmonic function      254
Hartman, P.      15 28 249 251 252 253 279
Heine — Borel theorem      40 52
Henderson, A.      154 160 276
hessian      103 119 231
Hewitt, E.      30 195 199 266 279
Higher order convexity      237
Hilbert space      51
Hirsch, W. M.      128 279
Hirschficld, R. A.      138 279
Hirschman, I. I.      224 225 279
Hoffman, A. J.      128 279
Holder, O.      8 279
Holder’s Inequality      191 193 194
Hopf, E.      237 240 280
Huggins, F.      28 266 280
Hukuhara, M.      224 225 280
Hyers, D. H.      256 257 257 280
Hyperplane      81
I-feasible form      158
Infinite dimensional space      42
Inner product      41 50 186
Interior point      40 47
Ioffe, A.      36 111 280
Isometric isomorphism      60
Isomorphic (isomorphism)      43
Jackson, D.      185 280
Jensen function      217
Jensen, J. L. W. V.      8 211 218 220 225 280
Jensen’s Inequality      89 189 213

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