Index 807Genetic algorithms, 3, 693, 694, 701
Genetic operators, 697
Geometric boundary conditions, 671
Geometric constraints, 7
Geometric programming, 3, 22, 492
applications, 525
arithmetic-geometric inequality, 500
complementary geometric
programming, 520
constrained problem, 508, 509
degree of difficulty, 496
mixed inequality constraints, 518
normality condition, 495
orthogonality conditions, 495
primal dual relations, 501
unconstrained problem, 493
Geometry of linear programming
problems, 124
Global criterion method, 764
Global minimum, 63
Goal programming method, 765
Golden mean, 270
Golden section, 270
Golden section method, 253, 267
Gomory’s constraint, 592
Gomory’s cutting plane method, 591
for all integer problem, 592
graphical representation, 589
for mixed integer problem, 599
Gradient, 95, 335
Gradient evaluation, 337
Gradient of a function, 335
Gradient methods, 335
Gradient projection method, 404
algorithm, 409
Graphical optimization, 10
Graphical representation, 589
Grid search method, 304, 314
H
Hamiltonian, 682
Helical spring, 22, 529
Helical torsional spring, 541
Hessian matrix, 71, 302
Heuristic search methods, 381
Historical development, 3
Hitchcock-Koopman’s problem, 221
Hollow circular shaft, 51
Hopfield network, 729
Huang’s family of updates, 353
Hydraulic cylinder design, 527
Hyperplane, 128I
Identifying optimal point, 140
Ill conditioned matrix, 306
Improving nonoptimal solution, 141
Inactive constraint, 94
Incremental response approach, 740
Independent events, 633
Independent random variables, 639
Indirect methods, 335, 380, 428
Indirect updated method, 361
Inequality constraints, 6, 93
Infeasibility form, 152
Infinite number of solutions, 148
Inflection point, 65
Initial value problem, 548
Input state variables, 546
Integer feasible solution, 610
Integer lattice points, 591
Integer linear programming, 589
Integer nonlinear programming, 606
Integer polynomial programming, 606
Integer programming, 3, 28, 588
Interior method, 222
Interior penalty function method,
432, 454
convergence proof, 438
extrapolation technique, 447
iterative process, 433
penalty parameter, 435
starting feasible point, 434
Interpolation methods, 253, 271
Interpretation of Lagrange multipliers, 90
Intersection of convex sets, 131
Intersection of fuzzy sets, 725
Interval halving method, 260
Interval of uncertainty, 256, 263
Introduction to optimization, 1
Inverse update formulas, 353
Inverted utility function method, 764
Iterative process of optimization, 252