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| Berkovitz L.D. — Convexity and Optimization in Rn |
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| Предметный указатель |
Saddle points, convex programming, necessary and sufficient conditions 182—188
Saddle points, game theory applications 125—127
Second derivative test, differentiable, unconstrained problems 130—133
Second-order conditions, differentiable, nonlinear programming 163—178
Second-order test vector, differential nonlinear programming 167—178
Sensitivity vector, convex programming, perturbation theory 193
Separation theorems 45—56
Separation theorems, alternative theorems 61—68
Separation theorems, best possible in  82—85
Separation theorems, disjoint convex sets 53—56 82
Separation theorems, point and convex set 49—53
Separation theorems, proper separation 46 53—54
Separation theorems, strict separation 46—47
Separation theorems, strong separation 47—49 54
Sequential criterion, Euclidean n-space  , limits 10—11
Simplex method, examples 222—225
Simplex method, extreme points, feasible set 225—229
Simplex method, phase I procedure 251—255
Simplex method, phase II procedure 234—245
Simplex method, preliminaries 230—234
Simplex method, revised method 255—260
Simplex method, termination and cycling 245—250
Slack variables, linear programming 144
Slack variables, simplex method, phase I 251—255
Smallest index rule, simplex method, termination and cycling 248—250
Strict local minimizers, defined 128
Strict local minimizers, differentiable nonlinear programming, second-order sufficient conditions 172—178
Strict local minimizers, differentiable unconstrained problems 130—136
Strict separation, convex sets 46—47
Strictly convex function, defined 87—88
Strictly convex function, differential criteria 109—111
Strong separation, convex sets 47—48
Subdifferentials, convex functions 102—106
Subgradients, convex functions 102—106
Subgradients, convex functions, differentiable functions 106—109
| Submarine-convoy game 124—127
Subsequences, continuity 9—11
Sufficient conditions, convex programming 181—187
Sufficient conditions, convex programming for absence of duality gap 206—207
Sufficient conditions, convex programming, quadratic programming 211
Sufficient conditions, differentiable nonlinear programming 159—160
Sufficient conditions, differentiable nonlinear programming, second-order conditions 172—178
Sufficient conditions, linear programming duality 218—219
Support function 101
Supporting hyperplanes 56—57 85
Supremum 12—14
Tableau method 236
Tangential constraints, differentiable nonlinear programming 165—178
Tangential constraints, differentiable nonlinear programming, second-order sufficiency theorems 172—178
Termination, simplex method 245—250
Theorems of the alternative, linear inequalities 61—68
Theorems of the alternative, linear inequalities, Farkas’s lemma 63—65 67—68
Theorems of the alternative, linear inequalities, Gale’s theorem 68
Theorems of the alternative, linear inequalities, Gordan’s theorem 65—67
Theorems of the alternative, linear inequalities, Motzkin’s theorem 66—67
Three-chord property, convex functions 92—94
Triangle inequality 3
Two-person zero-sum games 122—127
Unbounded sets, revised simplex method 259
Unbounded sets, simplex method 223 238—240
Unconstrained problems, differentiable problems 129—136
Unconstrained problems, linear regression 134—135
Unconstrained problems, orthogonal mean-square approximations 135—136
Unconstrained problems, second derivative test 130—133
Unconstrained problems, strict minimizers 130 132
Uniform continuity 117
Upper bounds, real numbers 11—14
Value function, perturbation theory 189—200
Vector-valued convex functions, alternative theorems 113—117
Von Neumann minimax theorem 117—121
‘‘Penalty function’’ proof, differentiable nonlinear programming 151—163
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