METHODS FOR FINDING FEASIBLE POINTS IN CONSTRAINED OPTIMIZATION

Methods for finding feasible points are needed in some numerical optim ization algorithms to initiate the search for a local minimum, Other m ethods perform more efficiently if a nearly feasible starting point is used. In addition, a feasible solution may be acceptable as the final design in some practical applications. Therefore, constraint correcti on methods are quite useful. Such methods based on penalty functions a nd primal approach are described and discussed. To gain insight into t he methods a two-variable problem is used to analyze the methods. Seve ral structural design problems are used to study the numerical behavio r of the methods and compare their performance. It is concluded that, in general, the primal methods are more efficient than the penalty fun ction methods. Also, no method has been found that is guaranteed to fi nd a feasible point for general constrained nonlinear problems startin g from an arbitrary point. In case a method fails, random points shoul d be used to restart the procedure to search for a feasible point.