Proximal Point Algorithm for Minimization of DC Function

Abstract

In this paper we present some algorithms for minimization of DC function (difference of two convex functions). They are descent methods of the proximal-type which use the convex properties of the two convex functions separately. We also consider an approximate proximal point algorithm. Some properties of the $\epsilon$-subdifferential and the $\epsilon$-directional derivative are discussed. The convergence properties of the algorithms are established in both exact and approximate forms. Finally, we give some applications to the concave programming and maximum eigenvalue problems.