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| Klatte D., Kummer B. — Nonsmooth Equations in Optimization: Regularity, Calculus, Methods and Applications |
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| Предметный указатель |
 -set of f 128
 -optimization problem 2
 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,  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, see “Piecewise ”
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 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 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 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,  -Frechet 66
Normal, vertical 67
Normal, vertical zero- 67
Normal, zero- 67
Open mapping theorem 85
Openness with linear rate 13
Optimality conditions 25 33 47
Parametric 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 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 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, -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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