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Nesterov Y. — Introductory Lectures on Convex Optimization: A Basic Course
Nesterov Y. — Introductory Lectures on Convex Optimization: A Basic Course

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Название: Introductory Lectures on Convex Optimization: A Basic Course

Автор: Nesterov Y.

Аннотация:

Nesterov (Center of Operations Research and Econometrics, Universitè Catholique de Louvain, Belgium) explains the main ideas of complexity theory for convex optimization, covering optimal methods and lower complexity bounds for smooth and non-smooth convex optimization. A separate chapter is devoted to polynomial-time interior-point methods. An undergraduate background in analysis and linear algebra is assumed. The book can be used for a one-semester course, and will be useful for industrial engineers and economists.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 254

Добавлена в каталог: 16.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $l_p$-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, $l_1$      116
Norm, $l_\infty$      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 $l_p$-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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