Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Bonnans F.J., Gilbert C.J., Lemarechal C. — Numerical Optimization
Bonnans F.J., Gilbert C.J., Lemarechal C. — Numerical Optimization

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Numerical Optimization

Авторы: Bonnans F.J., Gilbert C.J., Lemarechal C.

Аннотация:

Numerical Optimization has numerous applications in engineering sciences, operations research, economics, finance, etc. Starting with illustrations of this ubiquitous character, this book is essentially devoted to numerical algorithms for optimization, which are exposed in a tutorial way. It covers fundamental algorithms as well as more specialized and advanced topics for unconstrained and constrained problems. The theoretical bases of the subject, such as optimality conditions, Lagrange multipliers or duality, although recalled, are assumed known. Most of the algorithms described in the book are explained in a detailed manner, allowing straightforward implementation. This level of detail is intended to familiarize the reader with some of the crucial questions of numerical optimization: how algorithms operate, why they converge, difficulties that may be encountered and their possible remedies. Theoretical aspects of the approaches chosen are also addressed with care, often using minimal assumptions.


Язык: en

Рубрика: Математика/Оптимизация и управление/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 418

Добавлена в каталог: 22.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$C^{k,1}$      157
$C^{k}$      157
$I^{0}(x)$      154
$I^{0}_{*}, I^{0+}_{*}, I^{00}_{*}$      161
$O(\cdot)$, big O      163
$o(\cdot)$, little o      13 163
$\mathds{R}_{+}^{*}$      222
Adjoint equation      18
Adjoint state      18
Admissibility of the unit stepsize      48 63 253 264 278
Admissible      see "Set point"
Aggregation      116 119 122
Algorithm      see also "Method"
Algorithm bundle, dual      126
Algorithm bundle, general      118
Algorithm bundle, penalized      121
Algorithm level      120
Algorithm, Bunch & Kaufman      185
Algorithm, conjugate gradient      84 86
Algorithm, conjugate gradient, preconditioned      76
Algorithm, conjugate gradient, truncated      246 249
Algorithm, cutting-planes      112
Algorithm, descent      102
Algorithm, ellipsoid      111
Algorithm, Karmarkar      389
Algorithm, largest step      367
Algorithm, largest step, with safeguard      367
Algorithm, Newton      see "Newton's algorithm"
Algorithm, piecewise-linear search (PLS)      278
Algorithm, predictor-corrector      331
Algorithm, quasi-Newton      see "Quasi-Newton or secant (algorithm)"
Algorithm, simplex      302
Algorithm, subgradient      108
Algorithm, Uzawa      186
Analytic center      325 369
Armijo      47 80 84 118 241 250 251
Automatic differentiation      see "Computational differentiation"
Auxiliary problem principle      148
Basis matrix      302
BFGS      55 58 75 85 86 267
Bisection      40
Black Box      10 108
Bracket      39
Bunch & Kaufman      185
Bunch & Parlett      53
Bundle      117 123
Bundle, compression of      128
Canonical form of a linear complementarity problem      315
Central path      309 310
Central path, perturbed      346
Choleski      53
Code nlcv2      131
Coercive      100 148
Combinatorial optimization      3 10 142
Complementarity condition      141 160
Complementarity problem, linear      309
Complementarity, strict      161 315
complexity      383
Component of the Newton step, longitudinal      177
Component of the Newton step, transversal      177
Computational differentiation      18 20 89
Cone      162
Cone, critical      162
conjugate      see "Algorithm direction"
Constraint      3
Constraint equality      3
Constraint inequality      3
Constraint qualification      139 142
Constraint qualification, (A-CQ)      161
Constraint qualification, (LI-CQ)      161
Constraint qualification, (MF-CQ), of Mangasarian-Fromovitz      161
Constraint qualification, (S-CQ), of Slater      161
Constraint, active      4 152 154
Constraint, strongly active      161
Constraint, weakly active      161
Control      see also "Adjoint"
Control problem      4 7 8 16 178
control variable      7 16
Convergence in p steps      164
Convergence of bundle      133 134
Convergence of cutting-planes      113
Convergence of subgradients      109
Convergence, global      14 26 45 52 53 74 243 252
Convergence, linear      14 163
Convergence, local      166 182 183 195 207 210
Convergence, quadratic      14 164 201
Convergence, speed of      14 33 51 86 88
Convergence, superlinear      14 163 213
Convex      see "Set function problem"
Correction, Powell      270 274
Correction, second-order      256
Critical      see "Cone direction point"
Cubic fit      40
Curvature condition      267
Davidon, Fletcher & Powell      55
Decomposition of $\mathbb{R}^{n}$, by partitioning      178
Decomposition of $\mathbb{R}^{n}$, oblique      180
Decomposition of $\mathbb{R}^{n}$, orthogonal      179 201
Decomposition price      137 144
Decomposition price, algorithm      143
Decomposition resource      137
Decomposition, Benders      147
Decomposition, Dantzig — Wolfe      145
Dennis & More      60 63 82
Dilation      110
Direction      12 85
Direction of $\varepsilon$-descent      107
Direction of descent      29 75 97 108 235 264
Direction of steepest descent      30 103 105
Direction, affine      318
Direction, centralization      318
Direction, conjugate      69 74
Direction, critical      162
Direction, quasi-negative curvature      246
Directional derivative      95 158
Disaggregation      145
Divergent series      110
Duality      294
Duality, gap      98 139
Duality, weak      140 146
Elliptic      see "function"
Equivalent sequences      163
Everett      139
Existence of solution      159
Existence of solution, dual      138
Extrapolation      40 47
feasible      see "Set point"
Finite difference      101
Finsler      230
Fletcher (initialization of)      39 48
Fletcher — Reeves      73
Fromovitz      see "Constraint qualification"
Function penalty      217
Function, affine      4 26 83
Function, convex      25 26 57
Function, convex-concave      297
Function, dual      98 138
Function, elliptic      27 48 53 74
Function, exact      218
Function, inf-compact      25
Function, lower semi-continuous      25
Function, merit      13 29 37 79 217
Function, strongly      27 61 63 65 67
Gauss — Newton      83 86
Gauss — Seidel      29
Generalized Cauchy — Schwarz inequality      225
Globalization of an algorithm      217
Globalization of an algorithm by line-search      52 235
Globalization of an algorithm by trust regions      77
Gradient      3
Gradient, reduced      187
Group      313
Growth condition      27 33 46
hessian      3
Hessian of the Lagrangian      181
Identification      see "Parameter identification"
Inertia of a matrix      200
Inf-compact      see "Function"
Instability of cutting-planes      115
Instability of steepest-descent      104
Interpolation      40 242 251
Invariant      313
Karush, Kuhn, and Tucker (KKT)      see "Optimality conditions"
Lagrange multiplier      see "Multiplier"
Lagrangian      11 78 98 160 220 294
Lagrangian relaxation      10 98
Lagrangian, augmented      100 142 222 231 272
Length of a linear problem      384
Levenberg — Marquardt      83
Line-search      see also "Search" 12 72 77 78 109
Line-search, Armijo      241 251
Line-search, backtracking      242 250 251 270
Line-search, nonmonotone      263
Line-search, piecewise (PLS)      278
Line-search, watchdog      263
Line-search, Wolfe      see also "Wolfe conditions" 268
Linear complementarity problem      307
Linear complementarity problem, canonical form      315
Linear complementarity problem, monotone      309
Linear complementarity problem, standard form      314
Linearization error      123
Local minimum      see "Solution"
Mangasarian      see "Constraint qualification"
Maratos effect      254 271
master program      137 143 146
Matrix, basis      176
Matrix, right inverse      176 201
method      see also "Algorithm multiplier"
Method, local      170
Method, primal-dual      171
Minimax (finite)      99
Minimax (infinite)      99
Minimum      see "Solution"
Model      12 52 77 85 117
Model, cutting-planes      111 123
Model, cutting-planes, aggregated      128
Model, enriching      118
Modified field      322 323 352
Monotone      309
Multifunction      12
Multifunction, closed      13 106
Multifunction, locally bounded      13
Multifunction, outer semi-continuous      13
Multiplier      98 142 145
Multiplier first-order      189
Multiplier method      142
Multiplier, Lagrange      11 89 160 298
Multiplier, least-squares      183 189 201
Multiplier, second-order      189
Neighborhood      331
Neighborhood, large      311 340
Neighborhood, small      311 332
Newton's algorithm      39 79
Newton's algorithm for equality constrained problems, primal version      183
Newton's algorithm for equality constrained problems, primal-dual version      175
Newton's algorithm for equality constrained problems, reduced Hessian      193
Newton's algorithm for equality constrained problems, simplified Newton      194
Newton's algorithm for inequality constrained problems      see "Sequential quadratic"
Newton's algorithm programming for nonlinear equations      51 165
Newton's algorithm programming for unconstrained optimization      167
Nominal decrease      112 126
Norm      263
Norm associated with a scalar product      164
Norm, dual      225 232
Objective function      3 13 16
Optimal control      see "Control"
Optimal partition      302 315
Optimality conditions necessary, 1st order (NC1)      26
Optimality conditions necessary, 2nd order (NC2)      26 162
Optimality conditions necessary, Karush, Kuhn, and Tucker (KKT)      160
Optimality conditions necessary, reduced      190
Optimality conditions sufficient, 2nd order (SC2)      26 162
Optimality conditions sufficient, semi-strong 2nd order      163 231
Optimality conditions sufficient, strong 2nd order      163
Optimality conditions sufficient, weak 2nd order      163 231
Optimality system      298
Oscillation      31 104
Parameter augmentation      222
Parameter identification      6 82
Parameter penalty      225
Partition of variables      315
Penalization      see also "Function (penalty)"
Penalization, exact      218
Penalization, exact, $\ell_{1}$      232
Penalization, exact, augmented Lagrangian      218 223 233
Penalization, exact, Fletcher      231 263
Penalization, exact, Lagrangian      218 220
Penalization, exact, of the objective      218
Penalization, logarithmic      307
Piecewise line-search (PLS)      see "Line-search"
Pivoting      305
Point, basic      293
Point, basic, regular      304
Point, critical or stationary      26 27 52 82 161 297
Point, feasible or admissible      153
Point, interior      310
Point, optimal      97
Polak — Ribiere      73
Positive definite      26 27 67 82 83 86
Potential, Karrnarkar      389
Potential, logarithmic      307 325
Powell      see "Correction"
Preconditioning      34
Predicted decrease      49 80
Problem, ($P_{EI}$)      153
Problem, ($P_{E}$)      169
Problem, constrained convex      26 153
Problem, convex      139 142
Problem, dual      98 295 296
Problem, least-squares      201
Problem, linear      292
Problem, primal      97 138 296
Problem, saddle-point      296
Problem, tangent quadratic, of an equality constrained problem      172
Problem, tangent quadratic, of an inequality constrained problem      205
Problem, tangent quadratic, of an unconstrained problem      167
Problem,quadratic      292
Projection onto a convex set      164
Proximity measure      311 369
Quasi-Newton or secant algorithm, quasi-Newton SQP      270
Quasi-Newton or secant algorithm, reduced, for equality constrained problems      279
Quasi-Newton or secant equation      54 267
Quasi-Newton or secant matrix      54
Quasi-Newton or secant method      56 78 86
Quasi-Newton or secant method, poorman      75 84
Quasi-Newton or secant update criterion      281
Reduced cost      303
Reduced Hessian of the Lagrangian      175 188 191 200
Regular stationary point for equality constrained problems      175 200
Relative distance      376
Row/column generation      145
Saddle-point      98 220
Safeguard      41 368
Scaling      35
Search      see also "Line-search"
Search, curvilinear      85 119 120 275
Secant      see "Quasi-Newton"
Self-duality      357
Separating hyperplane      97 103
Sequential quadratic programming, (SQP) algorithm      151
1 2
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2019
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте