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Table 5.7.
Objective Subroutine lor (5.96) With Squared-Variable
Transformations
135 XCI) = SQR(X(I»
295 PRINT K; X(K).X(K); G(K)/(2.X(K»
935 PRINT K; X(K).X(K); G(K)/(2.X(K»
1000 REM BARRIER EXAMPLE (5.96) WITH SQUARED-
VARIABLE TRANSFORMATION
1005 R= I
1006 VI = X(l)..2
1007 V2 = X(2)..2
1010 Q=4,VI + V2+ R/VI +R/V2
1020 IF Y%=OTHEN F=Q
1030 IF Y%= I THEN F9=Q
1040 G(I)~4- R/VI..2
1050 G(2)~ 1- R/V2..2
1052 G(I)~G(I)'2.X(I)
1054 G(2)~G(2)'2.X(2)
1060RETVRN
Constraints 161
for each x and v component. This is employed in lines 1052-1054 to scale the
gradients for the optimizer's variable space, and in lines 295 and 935 to scale
the gradients to the outside world's variable space. The program should now
be run for the three previous cases to note that the positive-variable constraints
yield the correct optimum (Figure 5.30) from all starting points in the
first quadrant.
A number of bounding constraint transformations are shown in Table 5.8;
the first one is that employed above in (5.98). An interesting application of the
upper and lower bounds shown in Table 5.8 was suggested by Manaktala
(1972) and called "network pessimization." Suppose that a certain lowpass
network was constructed with elements having +(- tolerances. At each
Table 5.8.
Constraint
v;>O
v>O
V> vmin
v>vmin
-1