A new projective exact penalty function for a general constrained optimization

Abstract

A new projective exact penalty function method is proposed for the equivalent reduction of constrained optimization problems to unconstrained ones. In the method, the original objective function is extended to infeasible points by summing its value at the projection of an infeasible point on the feasible set with the distance to the set. The equivalence means that local and global minimums of the problems coincide. Nonconvex sets with multivalued projections are admitted, and the objective function may be lower semicontinuous. The particular case of convex problems is included. So the method does not assume the existence of the objective function outside the allowable area and does not require the selection of the penalty coefficient.