 -generalized gradient 249
 -algebra 306
-finite measure 306
Adjacent cone 126
Adjacent derivative 189
Adjacent epiderivative 237
Approximate selection 358
Asymptotic cone 159
Asymptotic epiderivative 300
atom 329
Attouch's theorem 299
Baire's theorem 44 58
Ball 17
Biorthogonal subspace 63
Bipolar cone 63
Bipolar set 63
Bipolar theorem 64
Bipolar theorem for closed convex processes 70
Bitranspose 67
Borel -algebra 306
Bounded family of processes 61
Bounded-valued map 36
Caratheodory map 311
Caratheodory parametrization 376
Caratheodory selection theorem 374
Castaing's theorem 319
Cellina's theorem 358
Characterization of monotone maps 107
Choquet's theorem 163
Circatangent cone 127
Circatangent cone to a sequence of sets 166
Circatangent derivative 189
Circatangent epiderivative 237
Clarke normal cone 157
Clarke tangent cone 127
Closed convex process 56 314
Closed convex set-valued map 34 373
Closed graph criterion 73
Closed graph theorem 60
Closed range theorem 64
Closed set-valued map 34 41
Closed-valued map 36 56
Coerciveness 88
Compact-valued map 36
Complementary convex 164
Complete -algebra 307
Complete -finite measure space 310
Complete measure space 307
Composition product 37
Concave function 222
Cone with compact sole 114
Conjugate function 256
Consistent 203
Consistent sequence of functions 96
Constrained inverse function theorem 96 207
Constraint qualification condition 140
Contingent cone 32 121
Contingent derivative 181
Contingent epiderivative 225
Contingent Hessian 299
Contingent hypoderivative 226
Contingently epidifferentiable 225
Continuous partition of unity 81 386
Continuous selection 355
Continuous set-valued map 40 141
Convergence of gradients 295
Convergence of subdifferentials 297
Convergence theorem 271
Convex epiderivative 241
Convex function 222
Convex hull of an upper limit 26 273
Convex kernel 159
Convex set-valued map 34 56
Convex-valued map 36
Core 36
Correspondence 33
COW 119
Criterion of pseudo-Lipschitzeanity 101
Crossed convergence 61
Curvaceous shape 354
Cut set-valued map 43
Dense family of selections 310
Derivable cone 127
Derivable set 127
Derivable set-valued map 182
Differential geometer 119
Differential quotient 94
Dini directional derivative 94
Directed set 19
Distance to a set 17
Domain 34
Dual norm 20
Duality map 125
Duality pairing 19
Duality relation 258
Dubovitskij — Miljutin cone 125
Eigenvalue of a convex process 114
Eigenvector of a convex process 114
Ekeland's rule 91 233
Epicontinuous 285
Epiderivative 225
Epigraph 222
Epilimit 275
Episleek function 225
Equilibrium map 207
Equilibrium theorem 84 276
Extension of a set-valued map 36 236
Extremal element 329
Extremal face 88 343
Extremal selection 330
Fenchel's inequality 256
Fermat's rule 232
Fixed point theorem for inward or outward maps 87 250
Frechet differentiable single-valued map 94 250
Gateaux differentiable single-valued map 94
Generalized gradient (Clarke) 249
Generalized sequence 19
Generic continuity 44
Generic property 44
God (spherical) 119
Gradient 94
Graph of a map 34
Graph of the transpose of a process 67
Graphical convergence 267
Graphical convergence of monotone maps 270
Graphical upper /lower limit of set-valued maps 267
Graves' theorem 95
Hausdorff distance 365
Higher order adjacent subset 171
Higher order circatangent subset 171
Higher order contingent subset 171
Higher order derivatives 216
Higher order epiderivatives 260
Hypertangent cone 164
Hypograph 222
Hypolimit 276
Image of a set-valued map 34
Indicator of a set 223
Inf-compact 281
Injective (globally) 209
Integrably bounded 326
Integral of a set-valued map 327
Intermediate cone 126
Invariant space 72
Inverse image 36
Inverse map 34
Inverse set-valued map theorem 204
Inverse stability theorem 100
Inward map 87
Kakutani's fixed point theorem 87
| Kernel of the derivative 187
Kruemmungsschwerpunkte 365
Ky Fan's inequality 80
Labor value 78
Lax's principle 96 99
Leray — Schauder's theorem 90
lim sup inf 192
Limit of infima 281
Limit of set-valued maps 41
Limit of sets 17
Linear extension of a set-valued map 346
Linear process 56
Lipschitz parametrization 379
Lipschitz selection 372
Lipschitz set-valued map 41
Local subdifferential 253
Local superdifferential 253
Local uniqueness criterion 103
Locally injective set-valued map 209
Lop-sided paratingent derivative 201
Lower Dini derivative 231
Lower epicontinuous 285
Lower epilimit 276
Lower hypolimit 276
Lower limit of set-valued maps 41
Lower limit of sets 17
Lower semicompact 281
Lower semicontinuity criterion 49
Lower semicontinuous set-valued map 39
Lower semicontinuously differentiable map 188
Lyapunov's Convexity theorem 339
Lyapunov's Convexity theorem (in Banach spaces) 340
Marginal function 48
Mathematical striptease 93
Maximal monotone map 106
Maximum theorem 48 258
Mazur's theorem 271
Measurable 307
Measurable (single-valued map) 307
Measurable selection 308
Measurable space 306
Measurable/Lipschitz map 373
Measurable/Lipschitz selection theorem 375
Michael's theorem 355
Minimal map 360
Minimal selection theorem 363
Minimum (bare) 93
Minkowski's difference of sets 159
Minty's theorem 108
Minty's trick 108
Monotone map 104
Moreau — Yosida's approximation 258
Moreau's theorem 258
Mosco's theorem 290
Multifunction 33 258
Multivalued function 33 270
Negative polar cone 63
Nonatomic measure 329
Nontrivial extended function 222
Nontrivial set-valued map 34
Norm of a process 57
Normal cone to a convex subset 139
Normal cone to a set 157
Open mapping theorem 57
Oresme — Fermat's rule 219
Orthogonal 63
Outward map 87
Paratingent cone 162
Paratingent cone to a sequence of sets 167
Paratingent derivative 201
Paratingent epiderivative 241
Poincare's continuation method 89 201
Point to set map 33
Pointwise convergence of set-valued maps 268
Pointwise inverse function theorem 101
Pointwise limit of set-valued maps 313
Polar cone 25 63
Polar of a viability domain 144
Polar set 28 63
Polish space 306
Positive polar cone 63 146
Positively homogeneous function 222
Positively homogeneous set-valued map 56
Process 56
Product of set-valued maps 37
Projection 125
Proper map 28
Proper set-valued map 43
Pseudo-convex function 233
Pseudo-convex set 145
Pseudo-convex set-valued map 182
Pseudo-Lipschitz set-valued map 41
Reflexive space 20
Residual 44 163
Resolvent of a monotone map 106
Restriction of a single-valued map 34 182
Robinson — Ursescu's open mapping theorem 58 194
Rocquefort 321
Sauterne 321
Selection of a set-valued map 355
Separable space 20
Separation theorem 64
Sequentially inf-compact 281
Sequentially weak upper limit 20
Set-valued Graves' theorem 205
Set-valued map 33
Shi Shuzhong's theorem 165
Simple map 307
simplex 82
Sleek set 101
Sleek set-valued map 182
Smooth Banach space 125
Sole of a cone 114
Solvability theorem 85 130
Square product of set-valued maps 37
Stability assumption 96
Stable family of set-valued maps 203
Star-shaped set 145
Steiner point 365
Strict set-valued map 34
Strictly convex space 360
Striptease (mathematical) 93
Strong convergence of a sequence in a Lebesgue space 272
Strong measurability 307
Subdifferential 248
Subgradient 248
Support function of a set 62
Support function of the transpose 75
Surjective closed convex process 57
Tangent cone to a convex cone 143
Tangent cone to a convex set 83 138
Tangent cone to a finite intersection 149
Tangent cone to a sleek subset 130
Tangent cone to direct image 153
Tangent cone to inverse image 148
Tangent cone to the interior of a set 140
Tangentially regular 127
Tarte Tatin 321
Transpose of a process 67
Transpose of a product 68
Transpose of the restriction 69
Transversality condition 32 96 147
Uniform boundedness theorem 61 152
Uniformly sleek set 101
Uniformly sleek set-valued map 205
Uniformly smooth 133
Unit ball 17 158
Upper epicontinuous 285
Upper epilimit 275
Upper hemicontinuous map 74 175
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