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Appendic C
III.
with
CRITERION FUNCTION WITH LINEAR FUNCTIONAL
CONSTRAINTS
minimize C(xi) for i = 1, 2 .... n
(C.4)
=
+ _- o
J
where
1. The criterion function is continuous and can be either linear or
non-linear
The criterion function is not automatically minimized for all the
variables equal to zero
IV. CRITERION FUNCTION WITH NON-LINEAR
CONSTRAINTS
minimize C(xi)
(C.6)
with
F~(xj) ---- 0 for
Fj(xj) > 0 and
and
xi= 1,2,...,n
where
1.
2.
j = ], 2 .... m
(C.7)
j=m+l .....
p
The criterion function and function constraints are continuous
The criterion function when properly constrained should not automatically minimize when all the variables are zero
V. TECHNIQUES FOR SOLUTION
There are dozens of algorithms for optimizing functions-none will work for
all cases, and all find local minima. The global minimum can be inferred by
finding local minima over a realistic range of the variables. Not all functions
will have a global minimum.
All of the techniques are iterative in nature and require repeated calculations of the criterion function, the gradient function, the Hessian matrix