CONTINUOUS DESCENT METHODS FOR THE MINIMIZATION OF LIPSCHITZ FUNCTIONS

Abstract

We study continuous descent methods for the minimization of Lipschitz functions defined on a general Banach space. We establish several convergence theorems for those methods which are generated by super-regular vector fields. Since we show that the complement of the set of super-regular vector fields is porous, we conclude that our results apply to most vector fields in the sense of Baire category.