An exact penalty function based on the projection matrix

Abstract

This paper proposes an exact penalty function based on the projection matrix concept. The proposed penalty function finds solutions which satisfy the necessary optimality conditions of the original problem. Some theoretical results are presented showing that every regular point provides an absolute minimum to the proposed penalty function if and only if it satisfies the necessary conditions of the original constrained problem. As a general rule, penalty functions may have spurious local minima. An advantage of the proposed penalty function is its ability to identify if an obtained minimum is spurious. The proposed penalty function was applied to solve equality constrained problems from the Hock–Schittkowski Collection. Some solutions were obtained more efficiently using the new penalty function than by using a conventional constrained optimization method.