R. A. SHANDIZ ET AL.

Copyright © 2011 SciRes. TEL

14

of feasible region. Thus, we suggest use of

such

that 1

. That is, use of the

with the order greater

than

O

is not recommended. Here, for having more

efficiency we suggest

=

for the penalty method

and

=

for the augmented Lagrangian method.

In Figure 1 number of function evaluations for the

ordinary penalty method (=0

) and new penalty me-

thod (=1

) is compared. The comparison of eva-

luations of ordinary augmented Lagrangian (=0

) and

new augmented Lagrangian (=12

) is illustrated in

Figure 2.

5. Conclusions

We proposed a simple modification to the penalty

methods and showed that the new penalty methods has

better performance than the usual penalty methods.

Computational results on several test problems showed

that number of iterations decreases and calculations

significantly reduce.

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