808 Index
J
Jacobian, 82
Joint density function, 639
Joint distribution function, 639
Jointly distributed random variables, 639
Joint normal density function, 646K
Karmarkar’s method, 222
algorithm, 226
conversion of problem, 224
statement of problem, 223
Kohonen network, 729
Kuhn-Tucker conditions, 98, 401
testing, 465L
Lagrange method, 85
necessary conditions, 86
sufficiency conditions, 87
Lagrange multipliers, 85, 675, 682
Lagrangian function, 86, 230
Learning process, 728
Lexicographic method, 765
Limit design of frames, 120
Linear convergence, 305
Linear extended penalty function, 451
Linearization of constraints, 387
Linearization of objective, 387
Linear programming, 3, 26, 119, 177
additional topics, 177
applications, 120
definitions, 127
theorems, 127
two phases, 150
Linear programming problem, 26
as a dynamic programming
problem, 569
geometry, 124
infinite solutions, 126, 148
matrix form, 122
scalar form, 122
standard form, 122
unbounded solution, 127, 146
Linear simultaneous equations, 133
Line segment, 128, 202
Local minimum, 63M
Machining economics problem, 525
Marginal density function, 639
Markov processes, 3
Marquardt method, 304, 348
Mathematical programming
techniques, 1, 3
MATLAB, 791
creating m-files, 793
defining matrices, 792
features, 791
introduction, 791
optimization toolbox, 793
special characters, 791
using programs, 794
MATLABsolutions, 37
binary programming problem, 624
constrained optimization problem, 474
goal attainment method, 767
interior point method, 235
linear programming problem, 156
one-dimensional problem, 294
quadratic programming problem, 237
unconstrained optimization
problem, 365
Matrix methods of structural analysis, 248
Maxwell distribution, 663
Mean, 635
Membership function, 723
Merit function, 9
Method of constrained variation, 77
Method of Lagrange multipliers, 85
Methods of feasible directions, 393
Methods of operations research, 2
Metropolis criterion, 703
MIMD architecture, 761
Minimum cost pipeline, 585
Minimum drag, 672
Mixed constraints, 453
exterior penalty function method, 455
interior penalty function method, 454
Mixed equality and inequality
constraints, 453
Mixed integer problem, 588
Model coordination method, 755
Modern optimization techniques, 3, 4, 693
Monotonicity, 547