METHODS FOR FINDING FEASIBLE POINTS IN CONSTRAINED OPTIMIZATION

Methods for finding feasible points are needed in some numerical optimization algorithms to initiate the search for a local minimum, Other methods 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 correction methods are quite useful. Such methods based on penalty functions and primal approach are described and discussed. To gain insight into the methods a two-variable problem is used to analyze the methods. Several structural design problems are used to study the numerical behavior of the methods and compare their performance. It is concluded that, in general, the primal methods are more efficient than the penalty function methods. Also, no method has been found that is guaranteed to find a feasible point for general constrained nonlinear problems starting from an arbitrary point. In case a method fails, random points should be used to restart the procedure to search for a feasible point.