An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization

Abstract

An implementable algorithm for solving a nonsmooth convex optimization problem is proposed by combining Moreau-Yosida regularization and bundle and quasi-Newton ideas. In contrast with quasi-Newton bundle methods of Mifflin et al. (1998), we only assume that the values of the objective function and its subgradients are evaluated approximately, which makes the method easier to implement. Under some reasonable assumptions, the proposed method is shown to have a Q-superlinear rate of convergence.