Engineering Optimization: Theory and Practice, Fourth Edition

Index 811

Reciprocal approximation, 685
Recurrence relationship, 551
Reduced basis technique, 737
Reduction ratio, 265
Reduction of size, 737
Refitting, 277
Reflection, 328
Reflection coefficient, 330
Reflection process, 329
Regression analysis, 3
Regular simplex, 328
Relative frequency of occurrence, 636
Relative minimum, 63
Reliability theory, 3
Renewal theory, 3
Reproduction, 697
Reservoir pump installation, 505
Reservoir system, 160
Return function, 546
Revised simplex method, 177
step-by-step procedure, 182
theoretical development, 178
Rigid frame, 120
Rocket in outer space, 16
Rosenbrock’s parabolic valley
function, 363
Rosen’s gradient projection method, 404
algorithm, 409
determination of step length, 407
projection matrix, 405
Roulette-wheel selection scheme, 698

S

Saddle point, 73
Scaffolding system, 26, 57
Scaling of constraints, 787
Scaling of design variables, 305, 787
Search with accelerated step size, 255
Search with fixed step size, 254
Secant method, 253, 290
Second level problem, 757
Second order methods, 305
Semidefinite matrix, 71
Sensitivity analysis, 207
Sensitivity equations, 751
using Kuhn-Tucker conditions, 752

using the concept of feasible

direction, 754

Sensitivity of optimum solution, 751

Sensitivity to problem parameters, 751

Separability, 547

Separability of functions, 31

Separable function, 31

Separable programming, 3, 31

Sequential decision problem, 544

Sequential linear discrete programming,

614

Sequential linear integer programming,

614

Sequential linear programming, 387

geometric interpretation, 388

Sequential quadratic programming, 422

derivation, 422

solution procedure, 425

Sequential unconstrained minimization,

431

Serial multistage decision process, 545

Shadow prices, 92

Shell and tube heat exchanger, 51

Side constraints, 7

Sigmoid function, 728

Signum function, 509

Simplex, 328, 384

Simplex algorithm, 139

flow chart, 143

Simplex method, 138, 304, 328

flow chart, 153

two phases, 150

Simplex multipliers, 180

Simply supported beam, 58

Simulated annealing, 3, 693, 702

Simulation methods, 3

Simultaneous equations, 133

Simultaneous search method, 257

Single stage decision problem, 546

Single variable optimization, 63

Slack variable, 123

Slider crank mechanism, 49

Solid body of revolution, 672

Solution by direct substitution, 76

Solution of linear equations, 133

Spring-cart system, 71

Stamping of circular discs, 49