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| Kiwiel K.C. — Methods of Descent for Nondifferentiable Optimization |
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| Предметный указатель |
Accumulation 133
Accuracy tolerance 58
Aggregate 34
Aggregate, approximation 56
Aggregate, distance measure 172
Aggregate, linearization 53
Aggregate, subgradient 34 53
Aggregation 51
Applicability 41
Approximation tolerance 307
Bisection 106
Bundle method 37 299
Caratheodory's theorem 3
Concave function 3
Cone 11
Constraint 1
Constraint, dropping 49
Constraint, function 1 22
Constraint, qualification 17
Constraint, violation function 206
Continuous diffentiability 1
contour 9
Convergence 42
Convex 2
Convex, combination 2
Convex, function
Convex, hull 2
Convex, outer approximation 11 29
Convex, problem 17
Convex, set 2
Cutting, idea 51
Cutting, method 25
Cutting, plane 25
Deletion rules 140
Descent 12
Descent, direction 12
Descent, method 22
Differentiable function 1
Direct search methods 1
Directional derivative 4
Directional derivative, generalized 4
Directional derivative, upper 4
Distance, measure 92
Distance, reset 92
Efficiency 41
Epigraph 3
Epigraph, Subdifferential 21
Epigraph, subgradient 21
F. John condition 17
feasible 19
Feasible, direction 19
Feasible, point method 22
Finite termination 76
Generalized directional derivative 4
Generalized gradient 6
Global convergence 42
Gradient 5
Gradient, type algorithm 1
Graph 9
Half-space 3
Hyperplane 3
Implementability 41
| Improvement function 191
Innex product
Interpolation 154
Kuhn — Tucker condition 17
Lagrange multipliers 49
Level set 10
Line search 29 47
Line segment 2
Linearization 9 10
Linearization, error 31 61
Linearization, updating 58
Local boundedness 6
Local solution 15
Locality 90
Locality, measures 32 90
Locality, radius 97
Locally lipschitzian
Lower approximation 10 11
Mathematical programming 1
max function 1
method 15
Method, of centers 192
Method, of flexible directions 218
Method, of linearizations 45
Method, of steepest descent 15
minimax 57
Nondifferentiable optimization 1
Nonlinear programming 1
Nonsmooth optimization 1
Norm 2
Null step 28
Objective function 1
Optimality condition 15 16 17
Phase I — phase II method 219 294
Polyhedral 26
Positive dependence 75
Powell's function 77
Projection 13
Rank 82
Reset 33
Selection 51
Selective approximation 53
Semismoothness 103 250
Serious step 28
Smooth problem 1
span 82
Stationarity measure 62 102
Stationary point 15 17
Steepest descent 15
stepsize 22
Stopping criterion 25
Strict differentiability 5
Strictly convex 3
Subdifferential 6
Subdifferential, regularity 6
Subgradient 6
Subgradient, algorithm 24
Supporting hyperplane 3
Trial point 28
Upper derivative 4
Upper semicontinuity 6
Weak semismoothness 105
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