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Fletcher R. — Practical methods of optimization. Volume 2: constrained optimization
Fletcher R. — Practical methods of optimization. Volume 2: constrained optimization

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Название: Practical methods of optimization. Volume 2: constrained optimization

Автор: Fletcher R.

Аннотация:

Fully describes optimization methods that are currently most valuable in solving real-life problems. Since optimization has applications in almost every branch of science and technology, the text emphasizes their practical aspects in conjunction with the heuristics useful in making them perform more reliably and efficiently. To this end, it presents comparative numerical studies to give readers a feel for possibile applications and to illustrate the problems in assessing evidence. Also provides theoretical background which provides insights into how methods are derived. This edition offers revised coverage of basic theory and standard techniques, with updated discussions of line search methods, Newton and quasi-Newton methods, and conjugate direction methods, as well as a comprehensive treatment of restricted step or trust region methods not commonly found in the literature. Also includes recent developments in hybrid methods for nonlinear least squares; an extended discussion of linear programming, with new methods for stable updating of LU factors; and a completely new section on network programming. Chapters include computer subroutines, worked examples, and study questions.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1981

Количество страниц: 224

Добавлена в каталог: 19.07.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$L_1$ approximation      7 9 41 172
$L_1$ exact penalty function      22 27 144 195
$L_\infty$ approximation      7 9 172
Acceleration technique      154
Active constraint      3 7 49 177
Active set      21 89
Active set method      vii; 4 7 13 20 26 42 88 90 92 110 149
Artificial constraint      26
Artificial variable      12 23 24
Artificial variable, method      22
Augmented Lagrangian function      131 151
Band matrix      88
Barrier function      128 145
Barrier function, inverse      129 153
Barrier function, logarithmic      129 154
Bartels — Golub method      30
Basic feasible solution (b.f.s.)      14 77
Basic feasible solution (b.f.s.), initial      15 23
Basic feasible solution (b.f.s.), optimal      14
Basic NDO      173 197 198 206
Basic variable      14
Basis matrix      14
Beale's method      85 101
BFGS formula      108 144 148 206
Big M method      27
Binding constraint      3
Bound      7 8 11 12 22 40 91 95 96 168
Branch and bound method      158
Branching variable      158
Broyden method      117
Bunch — Parlett factorization      88
Bundle methods      199
Canonical form      18
Combinatorial problem      157
Complementarity condition      51 98
Complementary pivoting      97
Composite function      174
Composite NDO      201
Concave function      66
Condition number      86
Conjugate directions      101 108
Conjugate gradient method      108 147
Conjugate subgradient method      199
Constrained NDO      178
Constraint function      1
Constraint qualification      54 55
contour      2
Convergence      170
Convergence, global      134 143 144 149 207
Convergence, linear      122 134
Convergence, second order      107 140 203
Convergence, superlinear      144
Convex combination      63
Convex function      64 166
Convex function, polyhedral      174
Convex hull      63
Convex programming problem      66 69 79 166
Convex set      63
Convexity      63
Courant penalty function      124
Curvature      5 58 65
Cutting plane method      201 207
Cycling      17 34 44 91
Dantzig two-phase method      158
Dantzig — Wolfe (QP) method      97
Dantzig — Wolfe decomposition method      32
Data fitting      172 202
Decomposition      20 28 32 172
Degeneracy      13 17 34 44 77 91 95
Degree of difficulty      167
Dependent equations      12
derivatives      3
Descent direction      47 55
Differentiable arc      47
Directional derivative      181 184 208
Directional sequence      47 52 61 211
Dual geometric programming problem      167
Dual norm      192
Dual problem      69 70 73 78
Dual transformation      11 69 166
Duality      69
EDGE      16
Elimination      5 6 15 80 106
Elimination method      4 6
Equality constraint problem      80 105 121 190
Equality constraints      1 80 105
Equality problem (EP)      89 92 110
Estimates (in integer programming)      161 163
Eta vector      28
Exact $L_1$ penalty function      22 27 144 195
Exact penalty function      8 22 27 143 151 190
Exchange algorithm      7
Exchange formula      94 95
Experimentation      1
Exterior penalty function      128
Extrapolation      126
Extreme point      13 64 77 78
Factorization      27
Farkas lemma      50 55
Feasible arc      62 145
Feasible arc search      149
Feasible correction      82
Feasible descent direction      46
Feasible direction      46 50 52 211
Feasible direction method      5 145
Feasible point      2 22 23 26 82 92 172
Feasible region      2
Finite difference approximations      3 5 107 108 110
Finite difference Newton method      107
First derivatives      3
First order conditions      6 51 52 68 117
First order necessary conditions      51 183 184
Gauss — Jordan product form      29 44
Gauss — Newton method      5 108 201
Generalized      81 86 88 106 146
Generalized chain rule      184
Generalized elimination method      81 86 88 106 146
Generalized gradient      184
Generalized inverse      47
Geometric programming problem      165
Global convergence      134 143 144 149 207
Global minimizer      67 93
Gradient projection method      88 108 147
Gradient vector      3
GRG method      147
Hessian matrix      3 58
Ill-conditioning      127 129 130 154
Inconsistent constraints      2 74 78
Indefinite QP      92 93
Inequality constraint problem      121 190
Inequality constraints      2 50 88 110 136 149
Infeasible problem      12 74
Initial      26 92
Initial basic feasible solution      15 23
Initial feasible point      26 92
Initial vertex      26 92
Integer feasible solution      158
Integer programming      157
Interior point method      128
Inverse barrier function      129 153
Isolated local minimizer      59 61 187
Jacobian matrix      3
Kuhn — Tucker (KT) conditions      51 68
Kuhn — Tucker (KT) point      51 93
Label      207
Lagrange multipliers      6 7 9 21 46 47 51 69 80 90 131 138 151 177 195
Lagrange multipliers, estimate      124 154
Lagrange multipliers, finite difference estimate      110
Lagrange multipliers, first order estimate      109 117 148
Lagrange multipliers, method of      7 47 86
Lagrange multipliers, second order estimate      109 117
Lagrange — Newton method      138
Lagrangian function      48 69 86 97 138
Lagrangian matrix      86 88 103 141 153
Lagrangian method      120
Large scale linear programming      27
Least distance problem      96
Least squares problems      108
Least squares solution      96
Lemke pivoting method      100
Levenberg — Marquardt parameter      143 149
Levenberg —Marquardt method      107 113
Lexicographic ordering      36
Line search      21 89 111 143 196
Linear approximations      5 138 139 151 201
Linear complementarity problem      98
Linear constraint programming      4
Linear constraints      4 63 79 105
Linear convergence      122 134
Linear function      4 66
Linear programming      4 11
Linear programming, dual      70
Linear programming, large scale      27
Linear programming, problem      11 63 67
Linear transformation      84
Linearization      5 138 139 151 201
Local convexity      69
Local minimizer      2 46 51 55 58 61 67 87 93 183
Locally Lipschitz function      174
Logarithmic barrier function      129 154
Maratos effect      206 211
max function      9 172 174
Maximization problem      2
Maximizer      48
Method of artificial variables      22
Method of Lagrange multipliers      7 47 86
Metric      87
Min-max approximation      9
Minimizer      46
Minimizer, global      67 93
Minimizer, isolated local      59 61 187
Minimizer, local      2 46 51 55 58 61 67 87 93 183
Mixed integer LP      157
Mixed integer programming      157
Model algorithm      207
Modulus function      9
Monotonic norm      192 211
Multiplier      see Lagrange multiplier
Multiplier penalty function      130 145 155
Newton — Raphson method      6 146 149
Newton's method      4 87 106 113 133 147 168
No-derivative methods      3 5 108
Non-basic variable      14
Non-differentiable optimization (NDO)      3 172
Non-linear      145
Non-linear elimination      145
Non-negative variable      11
Non-smooth optimization      3 172
Non-unique solution      16
Nonlinear programming      4 5 120 172
Nonlinear programming problem      69 194
Normal vector      3
Normalization constraint      167
Objective function      1
Optimal basic feasible solution      14
Optimality conditions      5
Orthogonal factorization method      84 86 87 91 106
Orthogonality constraint      167
Parametric programming      20 22 25 27 42 94
Parent problem      159
Penalty function      5 121
Penalty function, augmented Lagrangian      130 145 155
Penalty function, convergence      124
Penalty function, Courant      121
Penalty function, exact      8 22 27 143 151 190
Penalty function, exact $L_1$      22 27 144 195
Penalty function, exterior      128
Penalty function, multiplier      130 145 155
Penalty function, sequential      8
Perturbation method      35
Phase I      23 26 92
Phase II      23
Piece      175
Pivot      18 98
Polyhedral cone      56
Polyhedral convex function      174
Positive and negative variables      9 24
Positive definite matrix      58 66 69 79 87
Posynomial      165
Powell — Hestenes method      134 155
Primal problem      69 73
Principal pivoting method      98
Priorities      163
Product form method      13 28
Pseudo-constraint      21 26 92 94 95
QL method      202
Quadratic approximation      140 202
Quadratic function      66 79
Quadratic model      5
Quadratic Programming (QP)      4 79
Quadratic programming (QP), dual      72
Quadratic programming (QP), problem      63 67 79
Quadratic programming (QP), subproblem      137 139 140 150
Quadratic slack variable      8
Quadratic termination      101
Quasi-Newton method      4 107 112 134 143 149
Rank one correction      18 31 91
Reduced coordinate directions      81
Reduced costs      15 21
Reduced gradient method      85 147
Reduced gradient vector      82 106
Reduced Hessian matrix      82 106 147 206
Reduced quadratic function      82
Reduced variables      82
Regularity assumption      51 55 61 68 69 186 194
Reinversion      29
Residual      23
Restricted step method      5 107 113 143 205
Revised simplex method      13 18 33
Round-off enor      19 27 38 84 86 94
Saddle point      48
Scaling      9 90 196
Second derivatives      3
Second order conditions      58 69 87 117 132 189
Second order constraint qualification      62
Second order convergence      107 140 203
Second order necessary conditions      59 61 186
Second order sufficient conditions      61 132 141 187 192
Sensitivity      20
Separable function      152 168
Separable programming      152
Separating hyperplane lemma      57 181
Sequential minimization method      120 131
Sequential penalty function      8
Sherman — Morrison formula      18 155
Shortcut method      127
Simplex method      7 13 42
Simultaneous equations      172
Slack variable      8 11 21 24
Software      1
SOLVER method      138 140 202
Sparse linear programming      19 27 35
Sparse quadratic programming      85
Sparsity      19 27 35 85 108
Special ordered sets      157
Stack method      160
Standard form      11 23
Stationary point      46 49
Steepest descent      147 149
Steepest descent, method      198
1 2
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