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Bertsekas D.P. — Constrained Optimization and Lagrange Multiplier Methods
Bertsekas D.P. — Constrained Optimization and Lagrange Multiplier Methods



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Название: Constrained Optimization and Lagrange Multiplier Methods

Автор: Bertsekas D.P.

Аннотация:

This reference textbook, first published in 1982 by Academic Press, remains the authoritative and comprehensive treatment of some of the most widely used constrained optimization methods, including the augmented Lagrangian/multiplier and sequential quadratic programming methods. Among its special features, the book:
1) treats extensively augmented Lagrangian methods, including an exhaustive analysis of the associated convergence and rate of convergence properties
2) develops comprehensively sequential quadratic programming and other Lagrangian methods
3) provides a detailed analysis of differentiable and nondifferentiable exact penalty methods
4) presents nondifferentiable and minimax optimization methods based on smoothing
5) contains much in depth research not found in any other textbook


Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1 edition

Год издания: 1996

Количество страниц: 395

Добавлена в каталог: 12.04.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Active set approaches      248 279 285
Approximation procedures      167 312 376
Armijo rule      20
Armijo rule for minimax problems      197 201 292 297
Armijo rule for simple constraints      81
Augmented Lagrangian function      68 96 160 318
Broyden — Fletcher — Goldfarb — Shanno method      59 256
Chain rule      10
Cholesky factorization      17 46
Closed set      8
Compact set      9
Conjugate direction method      49
Conjugate gradient method      51
Conjugate gradient method, clustered eigenvalues      56
Conjugate gradient method, convergence      58
Conjugate gradient method, inaccurate line search      58
Conjugate gradient method, preconditioned      53
Conjugate gradient method, rate of convergence      54
Conjugate gradient method, restart      58
Conjugate gradient method, scaled      53
Continuous function      9
Continuously differentiable function      9
Convergence rate, linear      13
Convergence rate, order of      16
Convergence rate, Q-linear      15
Convergence rate, Q-superlinear      15
Convergence rate, sublinear      13
Convergence rate, superlinear      13
Davidon — Fletcher — Powell method      59 256
Dennis — Mor$\acute{e}$ condition      37
Descent direction      20
Direction of recession      329
Dual functional      125 317 319 367
Duality gap      317 371
Exact differentiable penalty functions      206 216
Exact differentiable penalty functions, automatic adjustment of penalty parameter      225
Exact differentiable penalty functions, choice of penalty parameter      221
Exact differentiable penalty functions, for inequality constraints      227
Exact differentiable penalty functions, for nonnegativity constraints      229
Exact nondifferentiable penalty functions      180 359
Exponential penalty function      310 313 314 364 376
Global minimum      19 67
Goldstein rule      21
Gradient      9
Gradient method      20
Gradient method, global convergence      24
Gradient method, local convergence      29
Gradient method, rate of convergence      30 35
Gradient method, stepsize selection      20
Gradient method, superlinear convergence      36
hessian      9
Implicit function theorem      11 12
Kantorovich Inequality      32
Lagrange multiplier      67 316
Lagrangian function      67 316
Lagrangian methods      231 234 240 243
Lagrangian methods, combined with differentiable exact penalty methods      260
Lagrangian methods, combined with nondifferentiable exact penalty methods      284
Lagrangian methods, combined with penalty and multiplier methods      258
Lagrangian methods, descent properties      237 263 266 272 275
Lagrangian methods, first order      232
Lagrangian methods, global convergence      257 272 275
Lagrangian methods, local convergence      232 235 242 247
Lagrangian methods, New'ton-like      234
Lagrangian methods, quasi — Newton versions      256 288
Lagrangian methods, rate of convergence      232 234 247 277 289
Limit inferior      8
Limit superior      8
Linearization algorithm      196 201 286
Linearization algorithm, convergence      198 203
Linearization algorithm, implementation aspects      204
Linearization algorithm, rate of convergence      205 234 248 289
Local minimum      19 66
Mean value theorem      11
Minimax problems      174 176 196 367
Multicommodity flow problems      49
Multiplier method      104 304 308
Multiplier method, computational aspects      121
Multiplier method, convergence      115 135 152 326
Multiplier method, duality framework      125 162
Multiplier method, finite convergence      349
Multiplier method, geometric interpretation      105 139
Multiplier method, inexact minimization      147 328
Multiplier method, one-sided inequality constraints      158
Multiplier method, partial elimination of constraints      141
Multiplier method, quasi — Newton versions      138
Multiplier method, rate of convergence      116 136 152 326
Multiplier method, second order      133 152 162
Multiplier method, stepsize analysis      126
Multiplier method, two-sided inequality constraints      164
Neighborhood      8
Newton’s method      40 234
Newton’s method for equality constraints      234
Newton’s method for inequality constraints      248 252
Newton’s method for simple constraints      90
Newton’s method in the space of primal variables      243
Newton’s method variations      240
Newton’s method, alternative implementations      235
Newton’s method, approximate      47
Newton’s method, descent properties      237
Newton’s method, periodic Hessian reevaluation      47
Nondifferentiable optimization      167 365
Norm      7
Open set      8
Ostrowski’s theorem      231
Penalty method      96 121
Penalty method, convergence      97 99 100 354
Penalty method, ill-conditioning      102
Penalty method, multiplier convergence      100 354
Penalty method, rate of convergence      355
Positive definite matrix      6
Positive semidefinitive matrix      6
Primal functional      105 113 317
Primal-dual method      153
Quadratic programming      184 186 197 202 248 252 287 288 291
Quasi — Newton methods, BFGS      59 256
Quasi — Newton methods, Broyden class      59
Quasi — Newton methods, computational aspects      63
Quasi — Newton methods, DFP      59 256
Quasi — Newton methods, for constrained problems      256 287 274
Quasi — Newton methods, Powell’s method      287
Quasi — Newton methods, rate of convergence      61 63 289
Quasi — Newton methods, self-scaling      64
Regular point      67
Scaling      39
Separable problems      154 157 364
Slater condition      317
Spacer step      38 58
Steepest descent      39
Subdifferential      316
Taylor series expansion      11
Unconstrained saddle point      326
Uniformly gradient related direction      24
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