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Klatte D., Kummer B. — Nonsmooth Equations in Optimization: Regularity, Calculus, Methods and Applications
Klatte D., Kummer B. — Nonsmooth Equations in Optimization: Regularity, Calculus, Methods and Applications

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Название: Nonsmooth Equations in Optimization: Regularity, Calculus, Methods and Applications

Авторы: Klatte D., Kummer B.

Аннотация:

"This book establishes links between regularity and derivative concepts of nonsmooth analysis and studies of solution methods and stability for optimization, complementarity and equilibrium problems." Audience: Researchers, graduate students and practitioners in various fields of applied mathematics, engineering, OR and economics. Also university teachers and advanced students who wish to get insights into problems, future directions and recent developments.


Язык: en

Рубрика: Математика/Оптимизация и управление/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 329

Добавлена в каталог: 23.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^{1}$-set of f      128
$C^{k}$-optimization problem      2
$PC^{1}$ function      5
Active functions      5
Asplund space      67
Aubin property      7
B-differentiable function      85
B-subdifferential      4
Barrier function      276
Berge-u.s.c. multifunction      10
Bouligand cone      106
Bouligand derivative      3
Boundary      1
C-stability system      168
Calmness      13
Clarke's directional derivative      3
Clarke's tangent cone      106
CLM set      16
Closed multifunction      2
Closure      1
Coderivative      3 66
Complete local minimizing set      16
Cone constraints      21 44
Cone constraints, standard      50
Cone, Bouligand      106
Cone, Clarke's tangent      106
Cone, contingent      64 106
Cone, normal      158
Conjugate function      92
Constant rank condition      31
Contingent cone      64
Contingent derivative      3 64 165
Convex hull      1
Critical point      150 152
Critical point, isolated      194
Critical value      150
Critical value function      222
Derivative, $D^{o}f$      4 127
Derivative, Bouligand      3
Derivative, Clarke's directional      3
Derivative, contingent      3 64 165
Derivative, directional      3
Derivative, generalized      3
Derivative, graphical      3
Derivative, injective      3 62
Derivative, partial C-      121
Derivative, partial T-      111
Derivative, strict graphical      3
Derivative, Thibault      165
Derivative, Thibault's      3
Describing function      19
Directional derivatives      3
Dirichlet's function      14
Dist      50
Domain of a multifunction      2
Ekeland's variational principle      303
Ekeland-point      38
Ekeland-point, global      38
Ekeland-point, local      38
Epi-convergence      17
Epsilon-normal to gphF      66
Epsilon-optimal      38
Error estimates      7
Exact penalty      95
Exact solutions      266
Exposed matrix      114
Extended MFCQ      57
Extreme value function      36
Feasible triple      266
Function, $PC^{1}$      see “Piecewise $C^{1}$
Function, B-differentiable      85
Function, barrier      276
Function, conjugate      92
Function, critical value      222
Function, describing      19
Function, exact penalty      95
Function, generalized Kojima-      151
Function, Kojima-      150
Function, Lagrange      150 184
Function, Lipschitzian increasing      19
Function, locally $PC^{1}$      128
Function, locally Lipschitz      1
Function, logarithmic barrier      277
Function, monotone NCP-      238
Function, NCP      5 236
Function, Newton      122
Function, penalty      94 276
Function, piecewise $C^{1}$      5
Function, pNCP      239
Function, pseudo-smooth      4 127
Function, semismooth      125 260
Function, simple      117
Function, standard Lagrange      150
Function, strongly monotone NCP-      237
Function, strongly semismooth      260
Functions, active      5
Gauvin's theorem      309
Generalized derivatives      3
Generalized equation      158
Generalized Jacobian      4 114
Generalized Kojima-function      151
Generalized LICQ      169
Generalized Newton method      258
Generalized semi-infinite optimization      21
Generalized strict MFCQ      170
Global Ekeland-point      38
Gordan's Theorem      308
Graph of a multifunction      2
Graphical derivative      3
Graves — Lyustemik theorem      10 85
Growth condition      81
Hausdorff-limit, lower      11
Hausdorff-limit, upper      11
Hoffman's lemma      29
Image of a multifunction      2
Implicit Lipschitz function      102
Injective derivative      3 62
Injectivity, with respect to u      205
Interior      1
Invariance of domain theorem      97
Inverse family      34
Inverse family of directions      35
Inverse Lipschitz function      100
Inverse multifunction      2
Inverse, local      34
Inverse, partial      42
Isolated critical point      194
Karush — Kuhn — Tucker point      150
KKT point      see “Karush — Kuhn — Tucker point”
Kojima-function      150
Kuratovski — Painleve limits      11
l.s.c. multifunction      10
Lagrange function      150 184
Lagrangian      150 184
LICQ      153 308
LICQ, generalized      169
Limit sets, Thibault's      3 62
Linearly surjecuve      64
Lipschitz continuous      11
Lipschitz l.s.c.      10
Lipschitz modulus      1
Lipschitz rank      1
Lipschitz u.s.c.      10
Lipschitzian increasing      19
Local Ekeland-point      38
Local inverse      34
Locally $PC^{1}$ function      128
Locally bounded      2
Locally compact      2
Locally Lipschitz      1
Locally u.L.      6 193
Locally upper Lipschitz      6 193
Locally upper Lipschitz at a set      13
Logarithmic barrier function      277
Lower Hausdorff-limit      11
Lower semicontinuous      10
Mangasarian — Fromovitz constraint qualification      7 49
Map, marginal      222
Map, Newton      122
Map, of normals      108
Map, projection      108
Marginal function      36
Marginal map      222
Matrix, exposed      114
Method, Wilson's      284
Metrically regular      12
MFCQ      7 49 308
MFCQ direction      49
MFCQ, extended      57
MFCQ, generalized strict      170
MFCQ, strict      31 308
Minkowski operations      1
Monotone NCP      5 236
Monotone NCP-function      238
Multifunction      see “Multivalued map”
Multifunction, Berge-u.s.c.      10
Multifunction, calm      13
Multifunction, closed      2
Multifunction, inverse      2
Multifunction, l.s.c.      10
Multifunction, Lipschitz continuous      11
Multifunction, Lipschitz l.s.c.      10
Multifunction, Lipschitz u.s.c.      10
Multifunction, local inverse      34
Multifunction, locally bounded      2
Multifunction, locally compact      2
Multifunction, locally u.L.      6 193
Multifunction, locally upper Lipschitz      6 193
Multifunction, locally upper Lipschitz at a set      13
Multifunction, lower semicontinuous      10
Multifunction, metrically regular      12
Multifunction, open with linear rate      13
Multifunction, partially invertible      42
Multifunction, pointwise Lipschitz      10
Multifunction, polyhedral      108
Multifunction, proper near a point      39
Multifunction, proto-differentiable      251
Multifunction, pseudo-Lipschitz      6
Multifunction, pseudo-regular      7
Multifunction, quasi-Lipschitz      50
Multifunction, strongly regular      7 61
Multifunction, u.s.c.      10
Multifunction, upper regular      7 63
Multifunction, upper regular at a set      13
Multifunction, upper semicontinuous      10
Multivalued map      2
Nash equilibrium      159
NCP      see “Nonlinear complementarity problem”
NCP function      5 236
NCP, monotone      5 236
NCP, standard      5 236
NCP, strongly monotone      5 236
Near x      1
Newton function      122
Newton map      122 258
Newton method      32 257
Nonlinear complementarity problem      5
Nonsmooth analysis      xi
Normal cone      158
Normal, $\varepsilon$-Frechet      66
Normal, vertical      67
Normal, vertical zero-      67
Normal, zero-$\varepsilon$      67
Open mapping theorem      85
Openness with linear rate      13
Optimality conditions      25 33 47
Parametric $C^{k}$ program      184
Parametric nonlinear program      184
Parametric program, with additional canonical perturbations      185
Parametric program, with canonical perturbations      185
Partial C-derivative      121
Partial inverse      42
Partial T-derivative      117
Partially invertible      42
Penalty function      94 276
Persistent regularity      72
Piecewise $C^{1}$ function      5
pNCP function      239
Point, critical      150 152
Point, KKT      150
Point-to-set distance      1
Pointwise Lipschitz multifunction      10
Polyhedral multifunction      108
Polyhedral set      108
Program, parametric $C^{k}$      184
Program, parametric nonlinear      184
Program, pseudo-regular      187
Program, strongly regular      187
Projection      108
Proper near a point      39
Proto-differentiable      251
Pseudo-Lipschitz      6
Pseudo-regular      7
Pseudo-regular linear systems      29
Pseudo-regular program      187
Pseudo-smooth function      4 127
Quasi-Lipschitz      50
Rademacher's Theorem      4
Rank, Lipschitz      1
Rank, of regularity      7
Regularity      6
Regularity, persistent with respect to G      72
Regularity, rank of      7
Selection property      202
Semismooth      125
Simple function      117
SOC      190
Solution, stationary      150 152
SQP-methods      275
SSOC      190
Stability system      168
Standard cone constraints      50
Standard NCP      5 236
Stationary solution      150 152
Strict graphical derivative      3
Strict MFCQ      31 308
Strongly monotone NCP      5 236
Strongly monotone NCP-function      237
Strongly regular      7 61
Strongly regular program      187
Strongly semismooth      260
Strongly stable in Kojima's sense      189
Subdifferential, $\varepsilon$-Frechet      38
Subdifferential, Clarke-      3
Subdifferential, convex      3
T-stability system      168
Theorem, Gauvin's      309
Theorem, Gordan's      308
Theorem, Graves — Lyusternik      10 85
Theorem, invariance of domain      97
Theorem, open mapping      85
Theorem, Rademacher's      4
Thibault derivative      3 62 165
Thibault's limit set      3
u.s.c. multifunction      10
Uniform rank of Lipschitz l.s.c.      34
Upper Hausdorff-limit      11
Upper regular      7 63
Upper regular at a set      13
Upper regular linear systems      29
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