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| Авторизация |
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| Поиск по указателям |
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| Nesterov Y. — Introductory Lectures on Convex Optimization: A Basic Course |
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| Предметный указатель |
Analytic center 198
Antigradient 17
Approximate centering condition 200
Approximation 16
Approximation, first order 16
Approximation, global upper 37
Approximation, in  -norms 226
Approximation, linear 16
Approximation, quadratic 19
Approximation, second order 19
Barrier, analytic 156
Barrier, self-concordant 193
Barrier, universal 212
Barrier, volumetric 156
Black box concept 7
Center, analytic 198
Center, of gravity 151
Central path 193
Central path, auxiliary 204
Central path, equation 193
Class of problems 6
Complexity, analytical 6
Complexity, arithmetical 6
Complexity, lower bounds 10
Complexity, upper bounds 10
Computational efforts 6
Condition number 65
Cone of positive semidefinite matrices 216
Cone of second order 214
Conjugate directions 43
Contracting mapping 30
Convex, combination 82 113
Convex, differentiable function 52
Convex, function 112
Convex, set 81
Cutting plane scheme 150
Damped Newton method 34
Dikin ellipsoid 182
Directional derivative 122
Domain of function 112
Epigraph 82
Estimate sequence 72
Feasibility problem 146
Function, barrier 48 180
Function, convex 112
Function, objective 1
Function, self-concordant 176
Function, strongly convex 63
Functional constraints 1
General iterative scheme 6
Gradient 16
Gradient, mapping 86
hessian 19
Hyperplane, separating 124
Hyperplane, supporting 124
Inequality, Cauchy — Schwartz 17
Inequality, Jensen 112
Infinity norm 116
Information set 6
Inner product 2
Kelley method 158
Krylov subspace 42
Level set 17 82
Localization set 141
Matrix, positive definite 19
Matrix, positive semidefinite 19
Max-type function 91
Method of analytic centers 156
Method of barrier functions 49
Method of centers of gravity 151
Method of conjugate gradients 42
Method of ellipsoids 154
Method of gradient 25
Method of inscribed ellipsoids 156
Method of penalty functions 47
| Method of uniform grid 8
Method of variable metric 38 40
Method of volumetric centers 156
Method, optimal 29
Method, path-following 202
Method, quasi-Newton 38
Minimax problem 91
Minimum, global 2
Minimum, local 2
Model of convex function 157
Model of minimization problem 5
Model of minimization problem, barrier 173 199
Model of minimization problem, functional 7
Newton method, damped 34 188
Newton method, standard 33 189
Newton system 33
Norm,  116
Norm,  8 116
Norm, Euclidean 16
Norm, Frobenius 216
Norm, local 181
Optimality condition, constrained problem 84
Optimality condition, first order 17
Optimality condition, minimax problem 92
Optimality condition, second order 19
Oracle, local black box 7
Oracle, resisting 10-11
Parameter, barrier 194
Parameter, centering 200
Performance on a problem 5
Performance on a problem class 5
Polar set 212
Polynomial methods 156
Positive orthant 213
Problem of approximation in -norms 226-227
Problem of geometric optimization 226
Problem of integer optimization 3
Problem of linear optimization 2 213
Problem of quadratic optimization 2
Problem of semidefinite optimization 216
Problem of separable optimization 224
Problem quadratically constrained quadratic 2 214
Problem smooth 2
Problem strictly feasible 2
Problem unconstrained 2
Problem, constrained 2
Problem, feasible 2
Problem, general 1
Problem, linearly constrained 2
Problem, nonsmooth 2
Projection 124
Quasi-Newton rule 40
Recession direction 211
Relaxation 15
Restarting strategy 45
Self-concordant, barrier 193
Self-concordant, function 176
Sequential unconstrained minimization 46
Set, convex 81
Set, feasible 2
Set, feasible, basic 1
Slater condition 2 49
Solution, global 2
Solution, local 2
Standard, logarithmic barrier 213
Standard, minimization problem 192
Standard, simplex 132
Stationary point 18
Step-size strategies 25
Strict separation 124
Structural constraints 3
Subdifferential 126
Subgradient 126
Support function 120
Supporting vector 126
Unit ball 116
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