Differential Constraint Scaling in Penalty Function Optimization

Abstract Penalty function optimization techniques are generally very successful in solving nonlinear programming problems. However, they can become computationally ineffective if certain of the constraints tend to dominate the entire constraint set. Under these circumstances, computational efficiency can often be restored by multiplying each constraint by an appropriate scale factor. This article presents a heuristic algorithm for computing such scale factors at periodic intervals during the computation. The method is applied to several sample problems, including some problems which are intentionally ill-scaled and others which are of a more realistic nature. The method is shown to be beneficial in all cases.