A redistributed proximal bundle method for nonsmooth nonconvex functions with inexact information

Abstract

In this paper, we propose a redistributed proximal bundle method for a class of nonconvex nonsmooth optimization problems with inexact information, i.e., we consider the problem of computing the approximate critical points when only the inexact information about the function values and sub gradients are available and show that reasonable convergence properties are obtained. We assume that the errors in the computation of functions and sub gradients are only bounded and in principle do not have to vanish within the limits. For the nonconvex functions, we design the convexification technique, which ensures that the linearization error of its augmentation function is non negative. Meanwhile, for the inexact information, we utilize noise management strategies and update approximate parameters to reduce the impact of inexact information. Based on this method, we can obtain the approximate solution.