A class of exact penalty functions and penalty algorithms for nonsmooth constrained optimization problems

Abstract

In this paper, a class of smoothing penalty functions is proposed for optimization problems with equality, inequality and bound constraints. It is proved exact, under the condition of weakly generalized Mangasarian–Fromovitz constraint qualification, in the sense that each local optimizer of the penalty function corresponds to a local optimizer of the original problem. Furthermore, necessary and sufficient conditions are discussed for the inverse proposition of exact penalization. Based on the theoretical results in this paper, a class of smoothing penalty algorithms with feasibility verification is presented. Theories on the penalty exactness, feasibility verification and global convergence of the proposed algorithm are presented. Numerical results show that this algorithm is effective for nonsmooth nonconvex constrained optimization problems.