812 Index
Standard deviation, 635, 636
Standard form of LP problem, 122
Standard normal distribution, 643
Standard normal tables, 643, 645
Starting feasible point, 434
State inversion, 566
Statement of an optimization problem, 6
State transformation, 546
State variables, 16
State vector, 679
Statically determinate truss, 542
Static optimization problem, 15
Stationary point, 65
Stationary values of functionals, 669
Statistical decision theory, 3
Statistically independent events, 633
Statistical methods, 3
Steepest ascent direction, 335
Steepest descent method, 304, 339
convergence criteria, 341
Step-cone pulley, 19
Step length determination, 398, 407
Stochastic process techniques, 3
Stochastic programming, 3, 29, 632
geometric programming, 659
linear programming, 647
nonlinear programming, 652
Structural error, 535
Structural optimization packages,
787
Suboptimization, 551
SUMT, 431
Superlinear convergence, 305, 361
Surplus variable, 124
Survival of the fittest, 696
Symmetric primal-dual relations, 192
System reliability, 583T
Taylor’s series expansion, 68, 642
Tentative solution, 670
Termination criteria, 401
Test functions (unconstrained nonlinear
programming), 363
Beale’s function, 365Brown’s badly scaled function, 365
Fletcher and Powell’s helical
valley, 364
Freudenstein and Roth function, 364
Powell’s badly scaled function, 365
Powell’s quartic function, 364
Rosenbrock’s parabolic valley, 363
Wood’s function, 365
Testing for concavity, 779
Testing for convexity, 779
Testing Kuhn-Tucker conditions, 465
Test problems (constrained nonlinear
programming), 467
heat exchanger, 473
speed reducer (gear train), 472
three-bar truss, 467
welded beam, 470
25-bar space truss, 468
Trajectory optimization problem, 16
Transformation techniques, 428
Transformation of variables, 381, 428
Transportation array, 221
Transportation problem, 177, 220
Transportation technique, 221
Transversality conditions, 682
Trapezoidal rule, 458
Travelling salesperson, 52
Trial, 254
Truss, 47, 55, 60, 248, 481, 487, 578, 623,
686, 691, 692, 741, 745, 758, 772
Tubular column design, 10, 654
Two-bar truss, 47, 55, 487, 533, 758
Two degree of difficulty problem, 526
Two phases of simplex method, 150
Two stage compressor, 67
Types of multistage decision
problems, 548U
Unbounded solution, 127, 142, 146
Unconstrained minimization (GMP), 493
Unconstrained optimization problem, 6,
301
Unconstrained optimization techniques,
301