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| Авторизация |
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| Bhatti M. — Practical Optimization Methods |
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| Предметный указатель |
Abel, M.L. 703
Active constraint 148
Active set method 535
Active set method for dual QP 552
Active set QP algorithm 538
ActiveSetDualQP function 554
ActiveSetQP function 539
ActiveSetQP function, options 539
Additive property of constraints 144
Aggregate constraint 144
ALPF algorithm 596
ALPF function 597
ALPF function, options 597
ALPF method 581
Analytical line search 232
AnalyticalLineSearch function 234
AnalyticalLineSearch function, options 234
Angle between vectors 79
Approximate line search, constrained 630
Approximate line search, unconstrained 251
Approximation using Taylor series 89
ArmijoLineSearch function 252
Armijo’s rule 251
Arora, J.S. 31 705
Artificial objective function 350
Augmented Lagrangian penalty function 590
Averiel, M. 420 705
Bahder, T. 703
Barrier function 588
Basic feasible solutions of LP 334
Basic idea of simplex method 339
Basic set, bringing a new variable into 341
Basic solutions of LP 334
BasicSimplex function 353
BasicSimplex function, options 353
BasicSolutions function 338
Bates, D.M. 13 705
Bazarra, M.S. 199 420 705
Beck, R.E. 420 706
Bertsekas, D.P 199 705
Beveridge 131 705
BFGS formula for Hessian 646
BFGS formula for inverse Hessian 289
Biegler, L.T. 645 647 705
Bland’s rule 371 390
Bontadelli, J.A. 18 706
Braselton, J.P. 703
Building design example, ALPF solution 604
Building design example, graphical solution 64
Building design example, KT solution 161
Building design example, problem formulation 2
Building design example, sensitivity analysis 180
Building design example, SQP solution 641
Capital recovery factor (crf) 21
Car payment example 22
Cash flow diagram 24
CashFlowDiagram function 24
Changes in constraint rhs 378
Changes in objective function coefficients 382
Cheng, R. 303 706
Choleski decomposition 564
CholeskiDecomposition function 566
Cofactors of a matrix 82
Coleman, T.F. 645 647 705
Combinatorial problems 303
Complementary slackness 151 439 497
Composite objective function 14
Compound interest formulas 19
Concave functions 113
Conjugate gradient method 262
Conjugate gradient method with non-negativity constraints 553
ConjugateGradient function 262
ConjugateGradient function, options 263
Conn, A.R. 645 647 705
Constant term in the objective function 317
Constraint function contours 50
Constraint normalization 582
Convergence criteria, interior point 451 508 522
Convergence criteria, unconstrained 228
Conversion to standard LP form 317
Converting maximization to minimization 137
Convex feasible sets 118
Convex functions 112
Convex optimization problem 121 502
Convex set 117
Convexity, check for complicated functions 113 116
ConvexityCheck function 122
Covariance 10
Covariance function 68
crf function 23
Cycling in LP 370
Dantzig, G.B. 420 705
Data fitting example, problem formulation 12
Data fitting example, solution using optimality conditions 142
Data fitting example, solution using QuasiNewtonMethod 299
Degarmo, E.P. 18 706
Degenerate solution 370
Dennis, J.E. 302 706
Descent direction 229 504 520 536 563
DescentDirectionCheck function 230
Design variables 2
Determinant of a matrix 80
Deville, Y. 303 706
DFP formula 288
Disjoint feasible region 61
Dual feasibility 467
Dual function 621
Dual LP problem 440
Dual QP for direction finding 620
Dual QP problem 497 620
Economic factors 24
Eigenvalues 84
Elementary row operations 320
Equal interval search 236
Equality (EQ) constraints 14
EquallntervalSearch function 237
Ertas, A. 31 706
Exact penalty function 590
Exterior penalty function 586
Fang, S.-C 481 706
Feasibility condition 151
Feasible region 50
Fiacco, A.V. 581 706
Fletcher — Reeves formula 262
Fletcher, R. 581 706
FormDualLP function 443
FormDualLP function, options 443
FormDualQF function 443
FormDualQF function, options 443
fSlack variables, or nonlinear problems 150
Gauss — Jordan form 320
GaussJordanForm function 324
Gen, M. 303 706
Genetic algorithm 303
Gill, P.E. 581 585 706
Global optimization 303
Glynn, J. 704
Golany, B. 420 705
Goldberg, D.E. 303 706
Golden ratio 3 243
Golden section search 243
GoldenSectionSearch function 244
Gomez, S. 581 706
Gordon, S.G. 131 705
Gradient condition 151
Gradient vector 92 95
Graphical optimization 16 47
Graphical solution, appropriate range for variables 49
GraphicalSolution function 57
GraphicalSolution function, options 58
| Gray, J.W. 704
Gray, T. 704
Greater-than type (GE) constraints 14
Hansen, E. 303 706
Hayhurst, G. 31 706
Hennart, J.-E 581 706
Hentenryck, P.V. 303 706
Hertog, D. 481 706
Hessian matrix 92 95
Hessian of Lagrangian 646
Hestenes, M. 302 706
Himmelblau, D.M. 302 706
http://www-c.mcs.anl.gov/home/otc/Guide/SoftwareGuide 420
Hymann, B. 31 706
Identity matrix 76 564
Inactive constraint 148
Inconsistent system of equations 325
Inequality constraint 14
Inflection point 133
Initial interior point 452 503
Interest functions 19
Interior penalty function 587
Interior point methods for LP 17 437
Interior point methods for QE 17 495 503
Inventory-carrying charges 7
Inverse barrier function 588 589
Inverse Hessian update 288
Inverse of a matrix 81
Investment risk 10
Jacobian matrix 100 622
Jahn, J. 131 706
Jeter, M.W. 131 706
Jones, J.C. 31 706
Karush — Kuhn — Tucker (KT) conditions 147
Karush — Kuhn — Tucker conditions, abnormal case 173
Karush — Kuhn — Tucker conditions, for LP 438
Karush — Kuhn — Tucker conditions, for QP 495 536
Karush — Kuhn — Tucker conditions, geometric interpretation of 165
Karush — Kuhn — Tucker point 151
Khachiyan, L.G. 481
Kolman, B. 420 706
KT conditions 147
KTSolution function 158
KTSolution function, options 159
Lagrange multipliers 150 498 536 552 591 621
Lagrange multipliers, recovering from LE 378
Lagrangian duality in NLP 199
Lagrangian for standard QP 496
Lagrangian function 150 552 591 621
Length of a vector 79
Less-than type (LE) constraints 14
Life cycle cost 18
Line search techniques 231
Linear independence of vectors 87
Linear programming (LP) 15 315 437
Linear system of equations 319
LinearAlgebra‘Choleski’ package 566
Linearization 608
Linearize function 609
Linearized problem 609
Local duality 199
Local maximum 133
Local minimum 133
Logarithmic barrier function 588 589
Lowe, M.J. 131 707
LU decomposition algorithm 330
LU decomposition, solving equations 328
LUDecompositionSteps function 332
Lueriberger, D.G. 420 706
Maeder, R. 704
Main diagonal of a matrix 76
Matrix 76
Matrix inverse identities 82
Matrix inversion using Gauss — Jordan form 327
Matrix operations 76
Matrix relationships 77
Maximization problem 14
Maximum constraint violation 628
McAloon, K. 131 707
McCormick, G.P. 581 706 707
Megiddo, N. 481 707
Merit function 628 647
Merit function, minimum of 630
Michel, L. 303 706
Minimization problem 14
Modified Newton method 272
ModifiedNewton function 273
ModifiedNewton function, options 273
Multiple objective functions 14
Multiple solutions 368
Murray, W. 581 585 706
Nash, S.G 199 420 707
Nazareth, J.L. 420 707
Necessary conditions 507 589
Necessary conditions, unconstrained problem 132
Negative values on constraint right-hand sides 317
Network problem 359
NewFUsingSensitivity function 177
Newton — Raphson method 100 465 520
NewtonRaphson function 101
Nicholls, R.L. 31 708
No feasible solution 365
Non-differentiable functions 302
Nonconvex functions 113
Nonconvex set 117
Nondegenerate solution 370
Nonlinear programming (NLP) 16 581
Normal to a surface 97
Null space 448 481
Null space, projection matrix 484 567
NullSpace function 484
Numerical methods for general NLP 581
Numerical methods for unconstrained 17 227
Objective function, adding a constant 136
Objective function, change using Lagrange multipliers 176 380
Objective function, contours 52
Objective function, rate of change of 176
Open top container example, KT solution and sufficient conditions 196
Open top container example, RSQP solution 651
Open-top rectangular container, problem formulation 29
Optimality conditions 552
Optimality conditions, finding an optimum using 134
Optimality conditions, for convex problems 181
Optimality conditions, for standard LP 438
Optimality conditions, for unconstrained problems 132
Optimality criteria methods 16 131
Optimization problem formulation 2
Optimization problem formulation, involving annual cost 29
Optimization problems, classification of 15
Optimization problems, solution methods 16
Optimization variables 2
OptimizationToolbox‘Chap3Tools’ package 90 101
OptimizationToolbox‘CommonFunctions’ package 87 96 110 122
OptimizationToolbox‘ConstrainedNLF package 597 609 615 632
OptimizationToolbox‘EconomicFactors’ package 23
OptimizationToolbox‘GraphicalSolution’ package 57
OptimizationToolbox‘InteriorPoint’ package 443 455 470
OptimizationToolbox‘LPSimplex’ package 324 332 338 353 393
OptimizationToolbox‘OptimalityConditions’ package 137 158 177
OptimizationToolbox‘Unconstrained’ package 230 234 237 241 244 249 252 254 262 273 289
Optimum of LP problems 319
OpttrnizationToolbox‘Quadratic Programming’ package 498 510 524 539 554
Ozan, T. 31 707
Padberg, M. 481 707
Pannell, D.J. 31 420 707
Papalambros, P.Y. 31 707
PAS algorithm for LP 454
PAS algorithm for QP 509
Penalty methods 585
Penalty number 586
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