Index
- A
- Absolute minimum, <em>57
- Acceptable point, <em>8
- ACO process as multi‐layered network, <em>653
- Active constraint, <em>8, 86
- Addition of constraints, <em>197
- Addition of new variables, <em>194
- Additive algorithm, <em>552
- Adjoint equations, <em>622
- Adjoint variable, <em>622
- Admissible variations, <em>71
- All‐integer problem, <em>537
- Analytical methods, <em>229
- Answers to selected problems, <em>777
- Ant colony optimization (ACO), <em>633, 652, 674
- algorithm, <em>655
- ant searching behavior, <em>653
- basic concept, <em>652
- evaporation, <em>654
- path retracing, <em>654
- pheromone trail, <em>654
- pheromone updating, <em>654
- Applications of dynamic programming, <em>526
- Applications of geometric programming, <em>480
- Approximate mean, <em>584
- Approximate variance, <em>584
- Arithmetic‐geometric inequality, <em>457
- Artificial variables, <em>127
- Augmented Lagrange multiplier method, <em>422
- equality‐constrained problems, <em>422
- inequality‐constrained problems, <em>423
- mixed equality‐inequality‐constrained problems, <em>425
- Augmented Lagrangian function, <em>422
- Availability of computer programs, <em>769
- Average, <em>578
- B
- Balas algorithm, <em>551
- Balas method, <em>551
- Barrier methods, <em>396
- Basic feasible solution, <em>119, 124
- Basic set operations, <em>661, 662
- Basic solution, <em>119, 124
- Basic variables, <em>124
- Basis, <em>119
- Basis vector approach, <em>704
- Beale's function, <em>332
- Beam‐column, <em>50
- Bearing, <em>486
- Behavior constraints, <em>7
- BFGS formula, <em>321
- BFGS method, <em>327
- Bias of random directions, <em>283
- Binary numbers, <em>554
- Binary programming, <em>750
- Binary variables, <em>553
- Bivariate distribution, <em>581
- Boltzmann's constant, <em>642
- Boltzmann's probability distribution, <em>642
- Boundary value problem, <em>501
- Bounded objective function method, <em>730
- Bound point, <em>8
- Brachistochrone problem, <em>612
- Bracket function, <em>406, 636
- Branch and bound method, <em>556
- Branching, <em>556
- Brown's badly scaled function, <em>332
- Broydon–Fletcher–Goldfarb–Shanno method, <em>327
- C
- Calculus methods, <em>3
- Calculus of variations, <em>3, 609
- Canonical form, <em>122
- Cantilever beam, <em>482
- Cauchy method, <em>308
- Cauchy's inequality, <em>457
- Central limit theorem, <em>589
- Chance constrained programming, <em>589
- Change in constraint coefficients, <em>195
- Change in cost coefficients, <em>192
- Change in right hand side constants, <em>188
- Characteristics of constrained problem, <em>347
- Checking convergence
- of constrained problems, <em>426
- perturbing the design vector, <em>427
- testing Kuhn–Tucker conditions, <em>427
- Choice of method, <em>767
- Circular annular plate, <em>629
- Classical optimization techniques, <em>57
- Classification
- of optimization problems, <em>14
- of unconstrained minimization methods, <em>276
- Classification of optimization problems based on
- deterministic nature of variables, <em>28
- existence of constraints, <em>14
- nature of design variables, <em>14
- nature of equations involved, <em>18
- number of objective functions, <em>31
- permissible values of design variables, <em>27
- physical structure of the problem, <em>15
- separability of the functions, <em>29
- Closed half space, <em>118
- Cluster analysis, <em>3
- Coefficient of variation, <em>579
- Collapse mechanism, <em>111
- Comparison
- of constrained methods, <em>768
- of elimination methods, <em>246
- of methods, <em>266
- of unconstrained methods, <em>767
- Complementary geometric programming, <em>475
- degree of difficulty, <em>478
- solution procedure, <em>477
- Complement of a fuzzy set, <em>662
- Complex method, <em>351
- Composite constraint surface, <em>8
- Computational aspects of optimization, <em>768
- Computer programs, availability of, <em>769, 770
- Computer program for
- ant colony optimization, <em>771
- fuzzy logic toolbox, <em>771
- genetic algorithm and direct search toolbox, <em>771
- modern optimization methods, <em>771
- multiobjective optimization, <em>772
- neural network toolbox, <em>771
- particle swarm optimization, <em>771
- simulated annealing algorithm, <em>771
- Concave function, <em>761
- Concept of cutting plane, <em>540
- Concept of suboptimization, <em>501
- Concrete beam, <em>28
- Condition number of a matrix, <em>277
- Cone clutch, <em>45, 483
- Conjugate directions, <em>289
- Conjugate gradient method, <em>310, 322
- Consistency condition, <em>200
- Constrained minimization (GMP), <em>508
- Constrained optimization problem, <em>6, 347
- characteristics, <em>347
- Constrained optimization techniques, <em>347, 348
- complex method, <em>351
- direct methods, <em>350
- indirect methods, <em>392
- random search methods, <em>350
- Constrained variation, <em>71
- Constraint qualification, <em>90, 91
- Constraints, <em>6
- Constraint surface, <em>7, 8
- Contact stress between cylinders, <em>269
- Contact stress between spheres, <em>228
- Continuous beams, <em>526
- Continuous dynamic programming, <em>523
- Continuous feasible solution, <em>556
- Continuous random variable, <em>576
- Contours of objective function, <em>10
- Contraction, <em>301
- Contraction coefficient, <em>302
- Control variables, <em>15
- Control vector, <em>619
- Convergence of constrained problems, <em>426
- by perturbing design vector, <em>427
- by testing Kuhn–Tucker conditions, <em>427
- Convergence of order p, <em>276
- Conversion of any 0‐1 problem to 0‐1 LP problem, <em>555
- Conversion of final to initial value problem, <em>517
- Conversion of nonserial to serial system, <em>500
- Convex
- Cooling fin, <em>616
- Correlation, <em>583
- Correlation coefficient, <em>583
- Correlation matrix, <em>589
- Covariance, <em>583
- Covariance matrix, <em>590
- CPM and PERT, <em>3
- Crane hook, <em>54
- Crisp set theory, <em>660
- Criterion function, <em>9
- Critical points, <em>711
- Crossover, <em>639
- Crow search algorithm, <em>680
- Cubic interpolation method, <em>253, 257
- Cumulative distribution function, <em>577
- Curse of dimensionality, <em>497
- Curve of minimum time of descent, <em>612
- Cutting plane, concept 540
- Cutting plane method, <em>540
- algorithm, <em>541
- geometric interpretation, <em>540
- Cyclic process, <em>301
- Cylinders in contact, <em>269
- D
- Dantzig, <em>109
- Darcy–Weisbach equation, <em>605
- Darwin's theory, <em>634
- Davidon–Fletcher–Powell method, <em>321
- DC motor, <em>48
- Decision variables, <em>6
- Decomposition principle, <em>159, 180
- Degenerate solution, <em>130
- Degree of difficulty, <em>453
- Derivatives
- of eigenvalues and eigenvectors, <em>707
- of static displacements and stresses, <em>705
- of transient response, <em>709
- Descent direction, <em>306
- Descent methods, <em>276, 304
- Design constraints, <em>7
- Design equations, <em>499
- Design of
- cantilever beam, <em>482
- column, <em>10
- cone clutch, <em>483
- continuous beams, <em>526
- drainage system, <em>529
- experiments, <em>3
- four bar mechanism, <em>489
- gear train, <em>528
- helical spring, <em>484, 601
- hydraulic cylinder, <em>482
- lightly loaded bearing, <em>486
- planar truss, <em>226
- two bar truss, <em>487
- Design point, <em>7
- Design space, <em>6
- Design variable linking technique, <em>698
- Design variables, <em>6
- Design variable space, <em>6
- Design vector, <em>6
- Determinantal equation, <em>65
- DFP formula, <em>320
- DFP method, <em>321
- Dichotomous search, <em>234
- Differential calculus methods, <em>229, 450
- Differential of f, <em>62
- Direction finding problem, <em>362
- Direction of steepest ascent, <em>304, 305
- Direct methods, <em>348, 350
- Direct root method, <em>259
- Direct search methods, <em>280
- Direct substitution, <em>69
- Discrete programming problem, <em>537
- Discrete random variable, <em>576, 577
- Discriminate analysis, <em>3
- Drainage system, <em>529
- Dual function, <em>458
- Duality in linear programming, <em>173
- Duality theorems, <em>176
- Dual problem, <em>173, 465
- Dual simplex method, <em>176
- Dual simplex algorithm, <em>177
- Dynamic programming, <em>3, 38, 497
- applications, <em>526
- calculus method of solution, <em>507
- computational procedure, <em>505
- continuous, <em>523
- conversion of final to initial value problem, <em>517
- problem of dimensionality, <em>572
- recurrence relation, <em>503
- tabular method of solution, <em>512
- E
- Eigenvalue, <em>65
- Electrical bridge network, <em>47
- Elementary operations, <em>122
- Elimination methods, <em>229, 231
- Elimination methods–comparison, <em>246
- Engineering applications of optimization, <em>5
- Engineering optimization literature, <em>34
- Equality constraints, <em>6, 69
- Equivalent deterministic NLP, <em>592
- Euler equation, <em>612
- Euler–Lagrange equation, <em>612
- Evaluation of gradient, <em>306
- Event, <em>576
- Exhaustive search, <em>229, 232
- Expansion, <em>301
- Expansion coefficient, <em>301
- Expected value
- continuous case, <em>578
- discrete case, <em>578
- Experiment, <em>576
- Extended interior penalty function, <em>414
- Exterior penalty function method, <em>406, 418
- algorithm, <em>408
- convergence proof, <em>410
- mixed equality‐inequality constraints, <em>416
- parametric constraints, <em>420
- Extrapolation of design vector, <em>410
- Extrapolation of objective function, <em>412
- Extrapolation techniques, <em>410
- design vector, <em>410
- objective function, <em>412
- Extreme point, <em>72, 119
- F
- Factor analysis, <em>3
- Failure mechanisms of portal frame, <em>222
- Fast reanalysis techniques, <em>700
- Basis vector approach, <em>704
- incremental response approach, <em>700
- Fathomed, <em>557
- Feasible direction, <em>87
- Feasible direction methods, <em>360
- Feasible solution, <em>119
- Feasible space, <em>8
- Fibonacci method, <em>238, 242
- flow chart, <em>242
- Fibonacci numbers, <em>239
- Final interval of uncertainty, <em>239, 246
- Final value problem, <em>501
- Finding the optimal values of design variables, <em>453
- Fireflies‐general information, <em>681
- behavior, <em>682
- light production, <em>682
- Firefly optimization, <em>675, 681
- First level problem, <em>723
- First order methods, <em>276
- Fitness function, <em>635, 636
- Fletcher and Powell's helical valley function, <em>331
- Fletcher–Reeves method, <em>310, 341
- iterative procedure, <em>311
- Floor design, <em>495
- Flow chart
- for augmented Lagrange multiplier method, <em>424
- for cubic interpolation method, <em>257
- for Fibonacci search method, <em>242
- for linear extended penalty function method, <em>415
- for Powell's method, <em>295
- for simplex algorithm, <em>131
- for simplex method, <em>140, 141
- for simulated annealing, <em>645
- for two‐phase simplex method, <em>140, 141
- Flywheel design, <em>441
- Forced boundary conditions, <em>612
- Four bar mechanism, <em>489
- Four bar truss, <em>55, 508
- Free boundary conditions, <em>612
- Free point, <em>8
- Freudenstein and Roth function, <em>331
- Fruitfly algorithm, <em>679, 683, 684
- Functional, <em>609
- Functional constraints, <em>7
- Function of a random variable, <em>580
- Function of several random variables, <em>583
- mean, <em>584
- variance, <em>584
- Fuzzy decision, <em>662
- Fuzzy feasible region, <em>663
- Fuzzy optimization, <em>633, 660, 662
- computational procedure, <em>663
- Fuzzy set, <em>661
- Fuzzy set theory, <em>660
- valuation set, <em>660
- Fuzzy systems, <em>660, 662
- G
- Game theory, <em>3
- Gaussian distribution, <em>585
- Gear train, <em>528
- General engineering design, <em>35
- General iterative scheme of optimization, <em>276
- Generalized penalty function method, <em>564
- choice of initial values of rk,k and βk , <em>566
- Generalized reduced gradient, <em>380
- Generalized reduced gradient method, <em>377
- algorithm, <em>380
- General NLP theory, <em>36
- General nonlinear programming, <em>36
- General primal dual relations, <em>174
- Genetic algorithms, <em>633, 640, 674
- representation of constraints, <em>635
- representation of design variables, <em>634
- representation of objective function, <em>635
- Genetic operators, <em>636
- crossover, <em>639
- mutation, <em>640
- reproduction, <em>637
- Geometric boundary conditions, <em>612
- Geometric constraints, <em>7
- Geometric programming, <em>3, 21, 37, 449
- applications, <em>480
- arithmetic‐geometric inequality, <em>457
- complementary geometric programming, <em>475
- constrained problem, <em>464
- constrained problem solution, <em>465
- degree of difficulty, <em>453
- differential calculus, <em>450
- mixed inequality constraints, <em>473
- normality condition, <em>452
- optimal values of design variables, <em>453
- orthogonality conditions, <em>452
- primal dual relations, <em>458
- unconstrained problem, <em>450
- Geometry of a cooling fin, <em>616
- Geometry of linear programming problems, <em>114
- George B. Dantzig, <em>109
- Global criterion method, <em>730
- Global maximum, <em>57
- Global minimum, <em>57
- Goal programming method, <em>732
- Golden mean, <em>245
- Golden section, <em>245
- Golden section method, <em>243
- Gomory's constraint, <em>541
- Gomory's method, <em>540
- solution procedure, <em>547
- Gomory's cutting plane method, <em>540
- for all integer problem, <em>541
- computational procedure, <em>542
- graphical representation, <em>542
- for mixed integer problem, <em>547
- Gradient, <em>87, 304
- Gradient evaluation, <em>306
- Gradient methods, <em>304
- Gradient of a function, <em>304
- Gradient projection method, <em>369
- algorithm, <em>374
- Graphical optimization, <em>13
- Graphical representation, <em>538
- Grid search method, <em>276, 285
- H
- Hamiltonian, <em>620
- Harmony memory size, <em>685
- Harmony search method, <em>677, 684
- Heat exchanger design, <em>435
- Helical spring, <em>21, 484
- Helical torsional spring, <em>495
- Hessian matrix, <em>65, 276
- Heuristics, <em>673
- Heuristic search methods, <em>348, 673
- Historical development, <em>3
- Hitchcock–Koopman's problem, <em>200
- Hollow circular shaft, <em>46
- Honey bee algorithm, <em>675, 689, 690
- bee colony, <em>689
- Honey bee swarm optimization, <em>689
- Hopfield network, <em>666
- Huang's family of updates, <em>321
- Hydraulic cylinder design, <em>482
- Hyperplane, <em>117
- I
- Identifying optimal point, <em>128
- Ill conditioned matrix, <em>277
- Imperialist competitive algorithm, <em>677, 680
- Improving nonoptimal solution, <em>129
- Inactive constraint, <em>86
- Incremental response approach, <em>700
- Independent events, <em>576
- Independent random variables, <em>582
- Indirect search methods, <em>304, 347, 392
- Indirect updated method, <em>328
- Inequality constraints, <em>6, 85
- Infeasibility form, <em>139
- Infinite number of solutions, <em>135
- Infinite‐stage or continuous problems, <em>523
- Inflection point, <em>59
- Initial value problem, <em>501
- Input state variables, <em>499
- Integer feasible solution, <em>556
- Integer lattice points, <em>540
- Integer linear programming, <em>538
- Integer nonlinear programming, <em>553
- Integer polynomial programming, <em>553
- Integer programming, <em>3, 27, 37, 537
- graphical representation, <em>538
- Integer programming methods, <em>538
- Integer representation in terms of binary variables, <em>553
- Intelligent water drops algorithm, <em>679
- Interior method, <em>202
- Interior penalty function method, <em>396, 416
- convergence proof, <em>402
- extrapolation technique, <em>410
- iterative process, <em>397
- penalty parameter, <em>399
- starting feasible point, <em>397
- Interpolation methods, <em>247
- Interpretation of Lagrange multipliers, <em>83
- Intersection of convex sets, <em>120
- Intersection of fuzzy sets, <em>662
- Interval halving method, <em>236
- Interval of uncertainty, <em>238
- Introduction to optimization, <em>1
- Inverse update formulas, <em>320
- Inverted utility function method, <em>730
- Iterative process of optimization, <em>229
- J
- Jacobian, <em>75
- Joint density function, <em>581
- Joint distribution function, <em>582
- Jointly distributed random variables, <em>581
- Joint normal density function, <em>588
- L
- Lagrange multiplier method, <em>77
- necessary conditions, <em>79
- sufficiency conditions, <em>80
- Lagrange multipliers, <em>77, 78, 615, 623
- interpretation, <em>83
- Lagrangian function, <em>78, 80
- Learning process, <em>665
- Levy distribution, <em>684
- Lexicographic method, <em>731
- Limit design of frames, <em>111
- Linear convergence, <em>277
- Linear extended penalty function, <em>414
- Linearization of constraints, <em>354
- Linearization of objective, <em>354
- Linear programming, <em>3, 25, 37, 109, 110
- additional topics, <em>159
- applications, <em>110
- definitions, <em>117
- post optimality analysis, <em>187
- sensitivity analysis, <em>187
- addition of constraints, <em>197
- addition of new variables, <em>194
- changes in constraint coefficients, <em>195
- changes in cost coefficients, <em>192
- changes in right hand side constants, <em>188
- theorems, <em>117
- two phases, <em>137
- Linear programming problem, <em>25, 112
- basic feasible solution, <em>119
- basic solution, <em>119, 124
- basis, <em>119
- as a case of dynamic programming problem, <em>519
- extensions, <em>159
- feasible solution, <em>119
- geometry, <em>114
- infinite solutions, <em>116, 135
- matrix form, <em>112
- nondegenerate basic feasible solution, <em>119
- optimal basic solution, <em>120
- optimum solution, <em>120
- scalar form, <em>112
- standard form, <em>112
- unbounded solution, <em>116
- Linear simultaneous equations, <em>122
- canonical form, <em>124
- pivot operation, <em>123
- pivot reduction, <em>123
- solution, <em>122
- Line segment, <em>117
- Local maximum, <em>57
- Local minimum, <em>57
- M
- Machining economics problem, <em>480
- Marginal density function, <em>582
- Markov processes, <em>3
- Marquardt method, <em>276, 316
- Mathematical programming problem, <em>9
- Mathematical programming techniques, <em>1, 3
- MATLAB®, <em>773
- creating m‐files, <em>775
- defining matrices, <em>774
- features, <em>773
- introduction, <em>773
- optimization toolbox, <em>775
- special characters, <em>773
- using programs, <em>776
- MATLAB® programs/functions for optimization problems, <em>740
- Binary programming problems, <em>750
- Constrained problems, <em>747
- General NLP problems, <em>740
- Linear programming problems, <em>742
- LP problems using interior point method, <em>743
- Multiobjective problems, <em>751
- One‐dimensional minimization problems, <em>746
- Quadratic programming problems, <em>745
- Unconstrained optimization problems, <em>746
- MATLAB® solutions, <em>739
- Matrix methods of structural analysis, <em>225
- Maxwell distribution, <em>604
- Mean, <em>578, 581
- Mechanical design, <em>35
- Membership function, <em>660
- Merit function, <em>9
- Meta, <em>673
- Metaheuristic algorithms, <em>39, 680
- Metaheuristic optimization methods, <em>673
- Metaphors, <em>673
- Method of constrained variation, <em>71
- Method of Lagrange multipliers, <em>77
- Methods of feasible directions, <em>360
- basic approach, <em>360
- Zoutendijk's method, <em>360
- Methods of operations research, <em>3
- Metropolis criterion, <em>642
- Military operations, <em>1
- Minimum cost pipeline, <em>534
- Minimum drag, <em>613
- Minimum weight design problem, <em>626
- Mixed constraints, <em>416
- exterior penalty function method, <em>418
- interior penalty function method, <em>416
- Mixed equality and inequality constraints, <em>416
- Mixed integer programming problem, <em>537
- Model coordination method, <em>722
- Modern methods of optimization, <em>4, 633
- Monotonicity, <em>500
- Motivation of simplex method, <em>127
- Multibay cantilever truss, <em>528
- Multilayer feedforward network, <em>666
- Multilevel optimization, <em>721
- Multimodal function, <em>231
- Multiobjective optimization, <em>9, 31, 38, 721, 729
- Bounded objective function method, <em>730
- Game theory approach, <em>733
- Goal attainment method, <em>732
- Goal programming method, <em>732
- Global criterion method, <em>730
- Inverted utility function method, <em>730
- Lexicographic method, <em>731
- Solution using MATLAB, <em>735
- Utility function method, <em>730
- Multiobjective programming, <em>3, 9, 31
- Multiobjective programming problem, <em>9, 31
- Multiple objective functions, <em>9
- Multistage decision problem, <em>497, 501
- Multistage decision process, <em>498
- Multistage decision representation, <em>499
- Multivariable optimization, <em>62
- with equality constraints, <em>69
- with inequality constraints, <em>85
- necessary conditions, <em>63, 74, 79, 86
- with no constraints, <em>62
- sufficiency conditions, <em>64, 76
- Multivariate distribution, <em>581
- Mutation, <em>640
- N
- Natural boundary conditions, <em>612
- Necessary conditions for optimal control, <em>619
- Negative definite matrix, <em>65
- Network methods, <em>3
- Neural network, <em>665
- Neural network based optimization, <em>633, 665
- Neuron, <em>665
- Newton method, <em>259, 276, 313
- Newton Raphson method, <em>260
- Node, <em>557
- Nonbasic variables, <em>124
- Nonconvex sets, <em>118
- Nondegenerate solution, <em>119
- Nongradient methods, <em>276
- Nonlinear programming, <em>3, 225, 273, 347
- Nonlinear programming problem, <em>18
- Nonpivotal variables, <em>124
- Nontraditional optimization techniques, <em>3, 39
- Normal distribution, <em>585
- Normality condition, <em>452
- Normalization condition, <em>578
- Normalization of constraints, <em>399
- Normalized beta function integrand, <em>565
- Norm of a matrix, <em>277
- Norm of a vector, <em>277
- Number of experiments, <em>247
- Numerical integration, <em>421
- O
- Objective function, <em>6, 9
- Objective function surfaces, <em>9
- Offspring, <em>639
- One degree of difficulty problem, <em>470, 481, 487
- One dimensional minimization methods, <em>225, 229
- comparison of methods, <em>266
- how to make them efficient, <em>265
- in multivariable problems, <em>266
- practical considerations, <em>265
- One‐stage policy, <em>504
- Operations research, <em>1
- methods, <em>3
- Optimal basic solution, <em>120
- Optimal control–necessary conditions, <em>619
- Optimal control problem, <em>37
- Optimal control theory, <em>609
- Optimality criteria methods, <em>622
- multiple displacement constraints, <em>624
- single displacement constraint, <em>623
- Optimal layout of a truss, <em>527
- Optimal solution (LP), <em>120
- Optimization, <em>1
- Optimization of fuzzy systems, <em>660, 662
- Optimization problems
- classification, <em>14
- statement, <em>6
- Optimization techniques, <em>3, 33
- Optimization toolbox, <em>739
- Optimum design variables, <em>466
- Optimum machining conditions, <em>480
- Orthogonal directions, <em>290
- Orthogonality conditions, <em>452
- Output state variables, <em>499
- Overachievement, <em>732
- P
- Parallel processing, <em>726
- Parameter optimization problem, <em>14
- Parametric constraint, <em>418
- exterior penalty function method, <em>422
- interior penalty function method, <em>420
- Parametric programming, <em>187
- Parent, <em>639
- Pareto optimum solution, <em>729
- Particle, <em>647
- Particle swarm optimization, <em>633, 647, 674
- alignment, <em>647
- cohesion, <em>647
- computational implementation, <em>648
- constrained problem, <em>649
- improvements, <em>649
- separation, <em>647
- Passing vehicle search algorithm, <em>677
- Pattern directions, <em>288
- Pattern recognition, <em>3
- Pattern search methods, <em>276, 288
- Penalty function, <em>394, 396, 406, 416, 636
- Penalty function method
- basic approach, <em>394
- convergence criteria, <em>399
- convergence proof, <em>402, 410
- exterior method, <em>406
- extrapolation, <em>410
- initial value of parameter, <em>398
- interior method, <em>396
- iterative process, <em>397, 408
- mixed equality and inequality constraints, <em>416
- normalization of constraints, <em>399
- parametric constraints, <em>418
- penalty parameter, <em>398
- starting feasible point, <em>397
- Penalty parameter, <em>398
- Performance index, <em>15, 619
- Perturbing the design vector, <em>427
- Phase I of simplex method, <em>137, 138
- Phase II of simplex method, <em>137, 139
- Pivot operation, <em>123
- Pivot reduction, <em>123
- Point in n‐dimensional space, <em>117
- Polynomial programming problem, <em>538
- Population, <em>634, 637
- Positive definite matrix, <em>65
- Positive semidefinite matrix, <em>65
- Post optimality analysis (LP), <em>187
- Posynomial, <em>21, 449
- Powell's badly scaled function, <em>332
- Powell's method, <em>276, 289
- algorithm, <em>293
- convergence criterion, <em>296
- flow chart, <em>295
- Powell's quartic function, <em>331
- Power screw, <em>52
- Practical aspects of optimization, <em>697
- Practical considerations (1‐d problem), <em>265
- Preassigned parameters, <em>6
- Precision points, <em>489
- Predual function, <em>457
- Pressure vessel, <em>53
- Primal and dual problems, <em>461
- Primal and dual programs, <em>466
- Primal dual relations, <em>173–175, 458
- Primal function, <em>457
- Primal problem, <em>173, 458
- Principle of optimality, <em>501, 503
- Probabilistic programming, <em>575
- Probability, definition, <em>575, 576
- Probability density function, <em>576, 577
- Probability distribution function, <em>577
- Probability distributions, <em>585
- continuous case, <em>585
- discrete case, <em>585
- Probability mass function, <em>577
- Probability theory, <em>575
- Problem of calculus of variations, <em>610
- Problem of dimensionality, <em>523
- Projected Lagrangian method, <em>388
- Projection matrix, <em>371
- Proportional damping, <em>710
- Pseudo dual simplex method, <em>553
- Q
- Quadratically convergent method, <em>290
- Quadratic convergence, <em>260, 277
- Quadratic extended penalty function, <em>415
- Quadratic form, <em>65, 81
- Quadratic interpolation method, <em>248, 252
- refitting scheme, <em>252
- Quadratic programming, <em>3, 23, 208
- Quadratic programming problem, <em>23
- Quasi‐Newton methods, <em>261, 276, 321
- Queueing theory, <em>3
- R
- Railroad track, <em>43
- Random jumping method, <em>280
- Random search methods, <em>276, 280, 283
- Random variable, <em>576
- Random walk method, <em>282
- Random walk with direction exploitation, <em>283
- Rank 1 updates, <em>319
- Rank 2 updates, <em>320
- Rate of change of a function, <em>307
- Rate of convergence, <em>276
- Real valued programming problem, <em>27
- Reanalysis, <em>700
- Reciprocal approximation, <em>625
- Recurrence relationship, <em>503
- Reduced basis technique, <em>697
- Reduction of size of optimization problem, <em>697
- Reduction ratio (in Fibonacci method), <em>241
- Refitting, <em>251, 256
- Reflection, <em>298
- Reflection coefficient, <em>300
- Reflection process, <em>299
- Regression analysis, <em>3
- Regular simplex, <em>298
- Relative frequency of occurrence, <em>577
- Relative maximum, <em>57
- Relative minimum, <em>57
- Reliability theory, <em>3
- Renewal theory, <em>3
- Reproduction, <em>637
- Reservoir pump installation, <em>462
- Reservoir system, <em>145
- Return function, <em>499
- Revised simplex method, <em>159
- step‐by‐step procedure, <em>164
- theoretical development, <em>160
- Rigid frame, <em>111
- Rocket in outer space, <em>16
- Rosenbrock's parabolic valley function, <em>330
- Rosen's gradient projection method, <em>369
- algorithm, <em>374
- determination of step length, <em>372
- projection matrix, <em>371
- Roulette‐wheel selection scheme, <em>637
- Runner‐root algorithm, <em>678
- S
- Saddle point, <em>67
- Salp swarm optimization, <em>675
- Scaffolding system, <em>25, 52
- Scaling of constraints, <em>770
- Scaling of design variables, <em>277, 770
- Search with accelerated step size, <em>232
- Search with fixed step size, <em>231
- Secant method, <em>229, 263
- Second level problem, <em>724, 727
- Second order methods, <em>276
- Semidefinite case, <em>65, 67
- Semidefinite matrix, <em>65, 67
- Sensitivity analysis (LP), <em>187
- addition of constraints, <em>197
- addition of new variables, <em>194
- changes in constraint coefficients, <em>195
- changes in cost coefficients, <em>192
- changes in right hand side constants, <em>188
- Sensitivity equations, <em>712
- using Kuhn–Tucker conditions, <em>712
- using the concept of feasible direction, <em>714
- Sensitivity of optimum solution, <em>712
- Sensitivity to problem parameters, <em>712
- Separability, <em>500
- Separability of functions, <em>29
- Separable function, <em>29
- Separable programming, <em>3, 29
- Sequential decision problem, <em>497
- Sequential linear discrete programming, <em>561
- Sequential linear integer programming, <em>561
- Sequential linear programming, <em>353
- geometric interpretation, <em>355
- Sequential quadratic programming, <em>386
- derivation, <em>386
- solution procedure, <em>389
- Sequential unconstrained minimization, <em>395
- Serial multistage decision process, <em>497
- Shadow prices, <em>84
- Shell and tube heat exchanger, <em>46
- Side constraints, <em>7
- Sigmoid function, <em>665
- Signum function, <em>465
- Simplex, <em>298
- Simplex algorithm, <em>128
- degenerate solution, <em>130
- flow chart, <em>131
- identifying optimum point, <em>128
- improving nonoptimal solution, <em>129
- infinite number of solutions, <em>135
- optimum solution, <em>131
- unbounded solution, <em>130, 134
- Simplex method, <em>109, 298
- contraction, <em>301
- contraction coefficient, <em>302
- expansion, <em>301
- expansion coefficient, <em>301
- flow chart, <em>140
- motivation, <em>127
- phase I, <em>138
- phase II, <em>139
- reflection, <em>298
- two phase, <em>137
- Simplex multipliers, <em>161
- Simply supported beam, <em>53
- Simulated annealing, <em>3, 633, 641, 645, 674
- Simulation methods, <em>3
- Simultaneous equations, <em>122
- Simultaneous search method, <em>233
- Single stage decision problem, <em>499
- Single variable optimization, <em>57
- necessary condition, <em>57
- sufficiency condition, <em>60
- Slack variable, <em>112
- Slider crank mechanism, <em>44
- Solid body of revolution, <em>613
- Solution by direct substitution, <em>69
- Solution of GMP problem
- using arithmetic‐geometric inequality, <em>457
- using differential calculus, <em>450
- Solution of linear equations, <em>122
- Solution of optimization problems using MATLAB, <em>739
- binary programming problems, <em>750
- constrained optimization problems, <em>747
- general NLP problems, <em>740
- linear programming problems, <em>742
- LP problems using interior point method, <em>743
- multiobjective optimization problems, <em>751
- one‐dimensional minimization problems, <em>746
- quadratic programming problems, <em>745
- unconstrained optimization problems, <em>746
- Spring‐cart system, <em>65
- Stamping of circular discs, <em>45
- Standard deviation, <em>578
- Standard form of LP problem, <em>112
- Standard normal distribution, <em>586
- Standard normal tables, <em>586, 587
- Starting feasible point, <em>397
- State inversion, <em>517
- Statement of an optimization problem, <em>6
- State transformation, <em>499
- State variables, <em>15
- State vector, <em>619
- Statically determinate truss, <em>496
- Static optimization problem, <em>15
- Stationary point, <em>59
- Stationary values of functionals, <em>610
- Statistical decision theory, <em>3
- Statistically independent events, <em>576
- Statistical methods, <em>3
- Steepest ascent direction, <em>304
- Steepest descent method, <em>276, 308
- convergence criteria, <em>310
- Step‐cone pulley, <em>18
- Step length determination, <em>364, 372
- Stochastic process techniques, <em>3
- Stochastic programming, <em>3, 28, 38, 575, 594
- constraints, <em>595
- geometric programming, <em>600
- linear programming, <em>589
- nonlinear programming, <em>594
- objective function, <em>594
- Structural error, <em>489
- Structural optimization, <em>34
- Structural optimization packages, <em>770
- Suboptimization, <em>506
- Sufficiency conditions <em>458
- SUMT, <em>395
- Superlinear convergence, <em>277, 328
- Surplus variable, <em>112
- Survival of the fittest, <em>635
- Symmetric primal‐dual relations, <em>173
- System of linear equations, <em>122
- pivotal reduction, <em>123
- pivot operation, <em>123
- solution, <em>122
- System reliability, <em>533
- T
- Tabular method of solution, <em>512
- Tabu search, <em>678
- Taylor's series expansion, <em>62, 584
- Teacher‐learning‐based optimization, <em>675
- Tentative solution, <em>610
- Termination criteria, <em>367
- Test functions (unconstrained nonlinear programming), <em>330
- Beale's function, <em>332
- Brown's badly scaled function, <em>332
- Fletcher and Powell's helical valley, <em>331
- Freudenstein and Roth function, <em>331
- Powell's badly scaled function, <em>332
- Powell's quartic function, <em>330
- Rosenbrock's parabolic valley, <em>330
- Wood's function, <em>332
- Testing for concavity, <em>761
- Testing for convexity, <em>761
- Testing Kuhn–Tucker conditions, <em>427
- Test problems (constrained nonlinear programming), <em>428
- heat exchanger, <em>435
- speed reducer (gear train), <em>433
- three‐bar truss, <em>429
- 25‐bar space truss, <em>430
- welded beam, <em>431
- Thermal system optimization, <em>35
- Trajectory optimization problem, <em>14
- Transformation techniques, <em>392
- Transformation of variables, <em>348, 392
- Transportation array, <em>201
- Transportation problem, <em>199
- Transportation technique, <em>201
- Transversality conditions, <em>622
- Trapezoidal rule, <em>421
- Travelling salesperson, <em>47
- Trial, <em>230
- Truss, <em>42, 50, 55, 226, 440, 443, 447, 528, 569, 626, 630, 631, 702, 706, 717, 724
- Tubular column design, <em>10, 596
- Two‐bar truss, <em>42, 50, 447, 487, 724
- Two degree of difficulty problem, <em>481
- Two phases of simplex method, <em>137
- Two stage compressor, <em>61
- Types of multistage decision problems, <em>501
- U
- Unbounded solution, <em>116, 130, 134
- Unconstrained minimization (GMP), <em>450
- test functions, <em>330
- Unconstrained optimization problem, <em>6, 273
- Unconstrained optimization techniques, <em>273, 276
- classification, <em>276
- general approach, <em>276
- Underachievement, <em>732
- Under‐reinforced beam, <em>29
- Uniform distribution, <em>585
- Unimodal function, <em>230
- Union of fuzzy sets, <em>661
- Univariate distribution, <em>581
- Univariate method, <em>276, 285
- Unrestricted search, <em>229, 231
- with accelerated step size, <em>232
- with fixed step size, <em>231
- Usable direction, <em>89
- Usable feasible direction, <em>360
- Utility function method, <em>730
- V
- Valuation set, <em>660
- Variable metric method, <em>321, 328
- Variance, <em>581
- Variation, <em>611
- Variational operator, <em>611
- Variation of a functional, <em>611
- Vector minimization problem, <em>729
- Vector of simplex multipliers, <em>162
- Venn diagram, <em>661
- Vertex, <em>117
- W
- Water evaporation optimization, <em>677
- Water resource system, <em>217
- Water tank design, <em>503
- Weighting function method, <em>730
- Weights, <em>457
- Well conditioned matrix, <em>277
- Wood's function, <em>332
- Z
- Zero degree of difficulty problem, <em>468, 480, 486
- Zero‐one LP problem, <em>555
- Zero‐one polynomial programming, <em>555
- Zero‐one problem, <em>538, 555
- Zero‐one programming problems, <em>537, 551
- Zeroth order methods, <em>276
- Zoutendijk's method, <em>348, 360
- determination of step length, <em>364
- direction finding problem, <em>362
- termination criteria, <em>367
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