Pallaschke D., Rolewicz S. — Foundations of Mathematical Optimization. Convex Analysis without Linearity :: Электронная библиотека попечительского совета мехмата МГУ

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Pallaschke D., Rolewicz S. — Foundations of Mathematical Optimization. Convex Analysis without Linearity

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Название: Foundations of Mathematical Optimization. Convex Analysis without Linearity

Авторы: Pallaschke D., Rolewicz S.

Язык:

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 598

Добавлена в каталог: 17.09.2012

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Предметный указатель

$(\Delta_{2})$ condition      58
$(\preceq A)$ , $(\prec A)$       500
$0^{+}$ -inner $\mathcal{F}$ -approximation      132 313
$0^{+}$ -outer $\mathcal{F}$ -approximation      132 313
$0^{+}$ -tangential $\mathcal{F}$ -approximation      132
$A\preceq$       500
$cl_\tau$       321
$cl_{\mathcal{R-}}$       52
$cl_{\mathcal{R}}$       52
$conv_{\Phi}$       26
$conv_{\Phi}^{\omega}$       26
$cos_{D}(h)$       540
$C^{n}$ - $\Phi$ -*.*      156
$DC(X), DCH(X), PC^{r}(U)$       413
$Der_{k,\delta}\mathcal{A}$       449
      55
$d^{g(t)}_{\Phi, F}$       118
$d_{x_{0}}^{Cl}{f}|$       355
$Epi_{f}$       22
$Epi_{f}^{0}$       22
$essInac\Gamma(y_{0})$       216
$Frac\Gamma(y_{0})$       19
$f\circ g$       296
$f\diamond g$       304
$f^{*}$       17
$f^{\Phi}$       4
$G(\Gamma)$       48
$G_{\varepsilon,\tau}(x_{0})$       479
$Hom_{\mathcal{A}}(\Omega_{\mathcal{A},k}, \mathcal{M})$       438
$Hyp_{f}$       304
$Hyp_{f}^{0}$       304
$Inac\Gamma(y_{0})$       214
$Ind_{A}$       294
$Int_\tau$       321
$Int_{\alpha}A$       31
$i_{K}(h)$       540
$K_{C}(x_0)^\tau$       321
$K_{C}(x_{0})$       317
$L_{r}(f)$ , $\overline{L}_{r}(f)$ , $L_{r}$ , $\overline{L}_{r}$       21
$Min_{f,\Gamma(y)}$       212
$PC^{r}(U)$ equivalent functions      456
$PC^{r}(U)$ -mapping      456
$P_\gamma(a,b)$       65
      52
$R_{x_{0}}^{C}f|$       363
      54
$S_{C}(x_{0})$       318
$T_{C}(x_{0})$       315
$T_{C}(x_{0})^\tau$       321
$x\ge\kappa\y$       49
$x\le\kappa\y$       49 503
$\alpha$ -cone      88
$\alpha$ -cone meagre set      88
$\delta$ -Hausdorff upper semi-continuous multifunction      199
$\delta$ -Lipschitz upper semi-continuous multifunction      199
$\Delta$ -uniformly convex norm      289
$\Delta_{2}$       58
$\frac{d_{\varepsilon}f}{dg}$       479
$\gamma$ -paraconvex function      303
$\mathcal{F}$ -stable multifuntion      174
$\mathcal{M}$ - $\Phi$ -differentiable      155
$\mathcal{M}in_{G}(y)$       543
$\mathcal{P}_\mathcal{R}^{—}(A)$       51
$\mathcal{P}_\mathcal{\overline{R}}(A)$       51
$\mathcal{T}_{C}(x_{0})$       316
$\mathcal{T}_{C}(x_{0})^\mathcal{T}$       321
$\overline{f\Gamma}(y)$       41
$\overline{R}$       ix
$\overline{\partial}f|_{x_{0}}$ , $\underline{\partial}f|_{x_{0}}$       442
$\parallel\cdot\parallel_{L}$       78
$\partial^{\Phi,0+} f$       113
$\partial^{\Phi,g(t),0+} f$       117
$\partial^{\Phi,loc} f$       99
$\partial^{\Phi} f$       3
$\partial_{loc}^{\Phi}f$       99
$\partial_{x_{0}}^{C}{f}|$       324
$\partial_{x_{0}}^{C}|$       324
$\partial_{\Phi,\mathcal{M}} f$       153
$\partial_{\Phi,\mathcal{M}}^{0+}} f$       153
$\partial_{\Phi,\mathcal{M}}^{p} f$       153
$\partial_{\Phi^{0+}} f$       113
$\partial_{\Phi^{g(t),+0}} f$       117
$\partial_{\Phi} f$       3
$\Phi$ -bump      115
$\Phi$ -bundle method      471
$\Phi$ -convex function      4
$\Phi$ -convex set      24
$\Phi$ -convex set weakly      23
$\Phi$ -convex vector      523
$\Phi$ -convexification      4 26
$\Phi$ -convexification vector      523
$\Phi$ -convexification weak      26
$\Phi$ -envelop      470
$\Phi$ -gradient      155 156
$\Phi$ -separated sets      37
$\Phi$ -subdifferential      3
$\Phi$ -subgradient      2 155 156 523
$\Phi$ -superdifferentiai      3
$\Phi$ -supergradient      2 155 156 523
$\Phi^{g}$ -bump      120
$\Phi_{0+}$ *.*      111
$\Phi_{conv}$       4
$\Phi_{g(t),0+}$ -*.*      117
$\Phi_{g(t),0+}$ -subgradient      117
$\Phi_{g(t),0+}$ -supergradient      117
$\Phi_{g(t),\varepsilon}-*.*$       117
$\Phi_{g(t)}$ -diffetential      118
$\Phi_{g(t)}$ -gradient Frechet      135
$\Phi_{min, loc}^{x_{0}}$       99
$\Phi_{min}$       8
$\Phi_{min}^{x_{0}}$       8
$\Phi_{\mathcal{M},0+}$ -*.*      153
$\Phi_{\mathcal{M}}$ *.*      152 153
$\Phi_{\varepsilon}$ -*.*      110 111
$\prec$       498
$\preceq$       497
$\stackrel{V}{inf} A$       522
$\stackrel{V}{sup} A$       522
$\varepsilon$ - $\mathcal{F}$ -tangential approximation      131
$\varepsilon$ - $\Phi$ *.*      10 11
$\varepsilon$ -conical neighbourhood of a set      130
$\varepsilon$ -inf-stationary point      479
$\varepsilon$ -inner approximation      131
$\varepsilon$ -outer approximation      130 313
$\varepsilon$ -tangential approximation      131
$\varepsilon-\partial^{\Phi} f$       11
$\varepsilon-\partial_{\Phi} f$       11
$\Xi$ - *.*      533 534 535 536
( $\varepsilon$ , $\tau$ )-stationary Pareto point      479
Abasov      15 551
Accumulation point of a filter      337
Active boundary of $\Gamma$ at $y_{0}$       190
Active constraints      344 383
Active index set      420
Active point      190
Alaoglu      229 551
Alexandroff      424 551
Algebraic *.*      31
Almost linear topological space      326
Almost lower semi-continuous multifunction      207
Angle-small set      88
Angleraud      71 234 235 236 238 551 555
Approximative quasidifferentiable function      459
Arc connected metric space      140
arg max      ix
Arg min      ix
arrow      506 551
Asplund      80 87 92 295 278 306 307 311 551
Attouch      67 297 301 304 551
Aubin      242 317 330 370 376 551

Auslender      67 551 552
Averbukh      156 552
Ayerbe      293 552
Aze      301 371 372 373 376 551 552
Balder      xi 50 57 184 552
Ball index of non-compactness      72
Banach      160 165 225 377 552
Banach — Steinhaus property      225
Bank      222 522
Barankin      506 551
Barbu      552
Barrier cone      242
Bartels      422 428 429 458 552
Basic homomorphism      434
Basis grill      338
Bednarczuk      67 213 214 215 216 217 218 219 544 552 553
Berge      180 553
Best gauge of well-condition      71
Best local growth condition      67
Bijective $PC^{r}(U)$ -mapping      456
Bijective QD(U)-mapping      456
Bilinear forms      390
Bilinear operator      390
Birkhoff      53 553
Birnbaum      58 553
Blackwell      506 551
Bliedtner      14
Borwein      120 121 200 208 211 553
Bouligand      317 553
Bronstedt      233 295 553
Cancelation law      298
Canonical coordinate transformation      455
Cegrell      553
Choquet      336 553
Chou      371 372 373 376 552 553
Clarke      332 355 357 358 360 361 412 553 554
Clarke derivative      355
Clarke derivative, recession cone      363
Clarke derivative, subdifferential      355
Clarke derivative, subgradient      355
Clarke derivative, tangent cone      332
Clarkson      242 279 554
Closed multifunction      192
Closed under max-min combination      414
Closedness with respect to the multifunction      51
Cominetti      67 551
Compact $\Phi$ -*.*      155
Complementarity condition      484
Completeness property      136
Cone generated by a set      36
Conjugate (Fenchel) function      17
Conjugate polarity      51
Containment property      544
Contingent cone      317 321
Contingent derivative of a multifunction      370
Continuous multifunction      202
Continuous multifunction, selection      420
Continuous multifunction, set covering problem      492
Controllable multifunction      375
Convex cone      33
Convex cone, multifunction      48
Convex cone, operator      49
Convex cone, process      48
Convex cone, set      29
Convexity      53
Cosine of a vector with respect to a cone      540
Couple      532
Craven      5 15 556
Critical point of quasidifferentiable function      457
Crouze      ix 67 551 552
Curve in a metric space      140
Cutillas      293 552
Cylindric function      10
Cylindric monotone multifunction      6 524
Danes      242 250 252 554
Dauer      497 554
Day      266 279 554
DC(X)-function      413
DC-function      413
DC-set      432
DCH(X)-function      413
Debreu      497 554
Decisively separated sets      133
Demyanov      441 464 468 554
Derivable set      317
Derivation into a modul      435
Derivation with respect to the basic mapping      435
Diepigraph polarity      55
Diepigraph polarity in a vector lattice      528
Difference quotient      151
Differentiable norm      116
Differential Frechet      135
Differential Frechet of order p      136
Directional $\Phi$ -*.*      156
Directionally decisively separated at $x_{0}$ sets      327
Dirichlet tessalation      493
Dolecki      xi 20 41 43 50 71 133 172 174 176 177 183 184 186 189 190 193 194 196 197 201 204 207 209 211 234 235 236 238 321 326 333 334 336 340 341 367 374 375 377 378 500 502 529 539 554 555
Dolecki approximations      367
dom f      ix
Domain of function      ix
Domain of multifunction      5 41
Domination property      502
Domination property, proper      547
Domination property, strong      547
Dominguez Benavides      293 552
Drop      242
Drop property      260
Drop property, weak      260
Drop, residual      280
Dual (Fenchel) function      12
Duality      42 43
Dubovitzkii      35 314 341 342 555
Dyadic stream      243
Edgeworth      555
Efficient point      503
Ekeland      64 115 138 242 551 555
Ekeland variational principle      63 64
Ellis      xi 555
Elster      20 555
Epigraph of a function      22 297
Epigraph of an operator      49
Equality level set      21
Equi-circatangent derivative of a multifunction      371
Essential active index set      420
Essential inner carrier      216
Essentially lower closed set      502
Essentially upper closed set      502
Extension condition      136
Extensive operator      52
Fan      xi 555
Federer      59 555
Fenchel      17 299 518
Fenchel conjugate (dual) function      17
Fenchel second dual function      20
Filter      337
Filter basis      337
Finite selection property      421
Foot-point      448
Frankowska      317 330 370 376 551
Frattini      452 555
Frattini algebra      452
Frechet      155 556
Frechet *.*      135 155
Frechet *.* differential of order n      393
Fujimura      493 556
Fukushima      488 556
g-convex set      53
g-differential Frechet      136
g-uniqueness property      119
Gateaux *.*      156

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