|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Auslender A., Teboulle M. — Asymptotic Cones and Functions in Optimization and Variational Inequalities |
|
|
|
| Предметный указатель |
Affine 2 89
Affine hull 2
Affine subspace 2 206
Asymptote 44
Asymptotic 36
Asymptotic approximation kernel 75 166
Asymptotic cone of function 55
Asymptotic cones 25—31
Asymptotic cones, dual characterization 31
Asymptotic cones, operations with 30
Asymptotic constraint qualification 134
Asymptotic direction 55 177
Asymptotic functions 47—60
Asymptotic functions as support functions 55
Asymptotic functions of conjugate 55
Asymptotic functions of maximal monotone maps 197 203 214
Asymptotic functions of spectral function 71
Asymptotic functions, calculus with 60
Asymptotic functions, convex cases. 50
Asymptotic functions, examples 51
Asymptotic functions, smoothing with 72
Asymptotic linear sets 36 93
Asymptotic optimality 229
Asymptotic polyhedral set 37
Asymptotically directional constant function 85
Asymptotically level stable function 94 99 162
Asymptotically linear function 94
Asymptotically well-behaved functions 124—132
Asymptotically well-behaved maximal monotone maps 219
Ball 3
Biconjugate 14 147
Biconjugate of marginal function 147 160
Bidual 148 149
Bipolar cone 6
Boundary 3
Boundary ray 44
Boundary relative 3
Bronsted — Rockafellar theorem 123
Caratheodory's theorem 3
Closed 2
Closed convex concave see convex-concave functionals
Closure 3 33
Closure criteria 33 46
Closure of sum of convex sets 39
Coercivity 81 160
Coercivity of maps 214
Coercivity, characterization 83
Coercivity, conditions 84
Coercivity, weak 85 129
Cofinite function 64
Compactness for convex problems 84
Compactness of optimal solution set 82
Compactness of primal dual solution sets 160
Complementarity 224
Complementarity problem 213
Cone 5
Cone barrier 18
Cone convex 5
Cone, finitely generated 8
Cone, generated by set 7
Cone, ice cream 68
Cone, normal 6
Cone, pointed 6 42
Cone, polar 6
Cone, polyhedral 7
Cone, tangent 7
Conical hull 7
Conjugate function 13 198
Conjugate function of marginal 147
Constancy space 55 160
Constancy space of infimal convolution 90
Constancy space, dual representation of 57
Constraint qualification 120 160
Continuous sets 33
Continuous sets, characterization of 45
Continuous sets, convex 44
Convex combinations 2
Convex feasibility problem 116
Convex functions 9—13
Convex hull of functions 13
Convex sets 1—8
Convex sets, operations with 2
Convex, hull 2
Convex-concave functionals 170
Convex-concave functionals, closed 173 194
Convex-valued maps 206
Directional derivative 15
Directional local boundedness 208
Domains and ranges 20 see
Dual objective 158
dual operations 108
Duality 13
Duality and asymptotic functions 166—170
Duality and stationary sequences 178—181
Duality for generalized equations 221
Duality for nonconvex problems 148
Duality for semidefinite optimization 169
Duality, abstract 145—153
Duality, conjugate 145 222
Duality, gap 150
Duality, perturbational 145
Duality, strong 151 160
Duality, weak 148 154 159
Effective domains 9
Ekeland's principle 85 122
Epigraph 9
Epigraph, operations with 9
Error bounds 125
Error bounds for convex systems 133
Error bounds, global 125
Error bounds, Lipschitz 140
Error bounds, local 125
Error bounds, sharp 134
Euclidean vector space 1
Extension map 207 210
Extreme 8
Extreme point 8
Extreme ray 8
Fenchel 14
Fenchel duality 154—157
Fenchel duality theorem 155
Fenchel inequality 14
Fenchel — Moreau theorem 14
Fenchel, duality 154
Gap function 213
Gauge function 60
Generalized equations 212 216
Generalized equations, solving 218
Graph of maps 184
Half-spaces 2
Helly's theorem 116
hessian 15
Hoffman's error bound 138
homogeneous functions 18
Hyperplane 2
Indicator function 11
Inf-projection 11
Infimal convolution 14 90
Inner product 1
Interior 3
Isotone 78 166
Jensen's inequality 11
| Krein — Milman theorem 8 37
Lagrangian duality 157—162
Lagrangian duality for VI problems 224
Legendre transform see conjugate
Level bounded function 83
Level sets 9
Level sets, operations with 9
Line segment principle 3
Lineality space 55
Linear mapping 3
Lipschitz functions 12 53
Lower semicontinuity 10
Lower semicontinuity of maps 22
lsc functions see lower semicontinuity
Marginal function 100 146 150 151 159
Marginal function for minimax problems 170
Matrix funtions 68
Maximal inonotonicity 183—186
Maximal monotone maps, compactness 211
Maximal monotone maps, convexity of 196
Maximal monotone maps, directional local boundedness 208
Maximal monotone maps, domains and ranges 195
Maximal monotone maps, locally bounded 211
Maximal monotone maps, range of sum 198
Maximal monotone maps, sum of 203
Metrically regular 139 140
Minimax theorems 175
Minimax theory 170 193
Minimax theory for convex-concave problems 173
Minimizing sequence see sequences
Minkowski — Weyl theorem 8
Minkowski's theorem 8
Minty's theorem 186
Monotone maps 184
Monotone maps, continuous 185
Monotone maps, Lipschitz 189
Monotone maps, local boundedness 206
Monotone maps, maximal 185
Monotone maps, nonexpansive 185 189
Monotone maps, resolvent 189 193
Monotone maps, single valued 184 189
Monotone maps, star 199
Monotone maps, strict 184
Monotone maps, strongly coercive 200
Multivalued maps 20
Nonexpansivity 185 193
Norm 1
Normal cone 192
Normal cone, formulas for 17
Normal cones see cone
Normal cones, operations with 112
Normal map 213
Optimality conditions 119
Optimality conditions, approximate 121
Optimality conditions, Fermat principle 120
Optimality conditions, KKT theorem 120
Optimality conditions, primal-dual 153
Orthant 6
Orthogonal complement 193
Orthogonal subspace 6
Palais — Smale condition 85 123
Perturbation function see marginal function
Piecewise linear quadratic 95
Pointed see cone
polar see cone
Polar, operations with 7
Polyhedral 7
Polynomial convex function 86
Positive hull 7 58
Positively homogeneous 18 58
Primal-dual problems 147 148
Projection 89 126 192
Proper functions 9
Proximal map 192
Recession directions 84
Relative interior see interior
Saddle 171
Saddle functions 171
Saddle points 171 177 193
Semibounded 42
Semibounded function 63
Semibounded set 42
Semibounded weakly 42
Semidefinite optimization 66
Semidefinite optimization, smoothing of 75
Separation 5
Separation of convex sets 5
Separation, polyhedral 7
Separation, proper 5
Separation, strong 5
Sequences 125
Sequences, asymptotically residual 140
Sequences, minimizing 125 142
Sequences, stationary 125 128 140 219
Set-valued maps 20—23
simplex 2
Slater's condition 120 160 170 228
Smoothing see asymptotic functions
Smoothing, examples of 75
Spectral functions 68
Stability 100
Stability, convex case 112
Stationary sequence see sequences
Strict convexity 11
Strong duality 151 153
Strong duality for minimax problems 175
Strong duality, dual attainment 151
Strong duality, primal attainment 153
Subdifferential 15 151 191 197 199 202 209
Subdifferential calculus 108 110
Subgradient 15 184 194 199
Sublinear function 18 78
Support functions 17—20
Supporting hyperplane 5
Symmetric functions 68
Symmetric matrices 67
Symmetric matrices, cone of psd 68
Symmetric matrices, eigenvalues of 68
Symmetric matrices, minimum eigenvalue 151
Tangent cone see cone
Upper semicontinuity 22
Upper semicontinuity of functions 82
Upper semicontinuity of maps 22
Upper semicontinuity of maximal monotone maps 211
Variational inequalities, dual problems 225
Variational inequalities, existence results for 213
Variational inequalities, Lagrangian for 218
Variational inequalities, primal-dual 223
Variational inequalities, problems 212
Variational inequalities, solutions set 216
Weak coercivity see coercivity
Weak coercivity of maps 215
Weak coercivity, characterization of 87
Weak duality see duality
Weak duality for minimax 171
Weakly analytic 163
Weakly analytic, convex programs 163
Weakly analytic, functions 163
Weierstrass theorem 82
Well-behaved functions see asymptotically
Well-behaved functions, dual characteriztion 130
Zero duality gap 150 151
Zero duality gap for special convex problems 16
|
|
|
| Реклама |
|
|
|
|
|
О проекте