810 Index
Particle swarm optimization (continued)
particle, 708
position, 708
velocity, 708
Pattern directions, 318
Pattern recognition, 3
Pattern search methods, 304
Penalty function, 696
Penalty function method:
basic approach, 430
convergence criteria, 435
convergence proof, 438, 447
exterior method, 443
extrapolation, 447
initial value of parameter, 435
interior method, 432
iterative process, 433, 445
mixed equality and inequality
constraints, 453
normalization of constraints, 436
parametric constraints, 456
penalty parameter, 431
starting feasible point, 434
Penalty parameter, 431
Performance index, 16, 679
Perturbing the design vector, 465
Phase I of simplex method, 151
Phase II of simplex method, 152
Pivot operation, 134
Pivot reduction, 135
Point in n-dimensional space, 128
Polynomial programming problem,
589
Population, 697
Positive definite matrix, 71
Positive semidefinite matrix, 71
Post optimality analysis, 207
Posynomial, 22, 492
Powell’s badly scaled function, 365
Powell’s method, 304, 319
algorithm, 323
convergence criterion, 326
flow chart, 325
Powell’s quartic function, 364
Power screw, 57
Practical aspects of optimization, 737
Practical considerations, 293Preassigned parameters, 6
Precision points, 535
Predual function, 500
Pressure vessel, 59
Primal and dual programs, 505, 510
Primal dual relations, 193, 501
Primal function, 500
Primal problem, 192, 509
Principle of optimality, 549
Probabilistic programming, 632
Probability, definition, 632, 633
Probability density function, 633
Probability distribution function, 634
Probability distributions, 643
Probability mass function, 634
Probability theory, 632
Problem of dimensionality, 572
Projected Lagrangian method, 425
Projection matrix, 405
Proportional damping, 749
Pseudo dual simplex method, 606Q
Quadratically convergent method, 319
Quadratic convergence, 287, 305, 325
Quadratic extended penalty function, 452
Quadratic form, 71
Quadratic interpolation method, 253, 273
Quadratic programming, 3, 24, 229
Quasi-Newton condition, 304
Quasi-Newton method, 253, 288, 350
Queueing theory, 3R
Railroad track, 48
Random jumping method, 311
Random search methods, 304, 309, 383
Random variables, 633
Random walk with direction
exploitation, 313
Random walk method, 312
Rank 1 updates, 351
Rank 2 updates, 352
Rate of change of a function, 338
Rate of convergence, 305
Real valued programming problem, 28
Reanalysis, 740