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Bhatti M. Practical Optimization Methods
Bhatti M.  Practical Optimization Methods









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: Practical Optimization Methods

: Bhatti M.

:

Textbook presenting basic optimization theory in a concise manner suitable for students in all branches of engineering, operations research, and management information systems. Approaches the subject from both a theoretical and mathematical style.


: en

: /

:

ed2k: ed2k stats

: 2000

: 715

: 16.07.2005

: | | ID
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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
Armijos 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
Blands 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
LinearAlgebraCholeski 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
OptimizationToolboxChap3Tools package      90 101
OptimizationToolboxCommonFunctions package      87 96 110 122
OptimizationToolboxConstrainedNLF package      597 609 615 632
OptimizationToolboxEconomicFactors package      23
OptimizationToolboxGraphicalSolution package      57
OptimizationToolboxInteriorPoint package      443 455 470
OptimizationToolboxLPSimplex package      324 332 338 353 393
OptimizationToolboxOptimalityConditions package      137 158 177
OptimizationToolboxUnconstrained package      230 234 237 241 244 249 252 254 262 273 289
Optimum of LP problems      319
OpttrnizationToolboxQuadratic 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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