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| Fletcher R. — Practical methods of optimization. Volume 2: constrained optimization |
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| Предметный указатель |
 approximation 7 9 41 172
exact penalty function 22 27 144 195
 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 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 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
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