Trust region method for nonsmooth convex optimization

Abstract

We propose an iterative method that solves a nonsmoothconvex optimization problem by converting the originalobjective function to a once continuously differentiablefunction by way of Moreau-Yosida regularization.The proposed method makes use of approximate functionand gradient values of the Moreau-Yosida regularizationinstead of the corresponding exact values.Under this setting, Fukushima and Qi (1996) and Raufand Fukushima (2000) proposed a proximal Newton method anda proximal BFGS method, respectively, for nonsmooth convex optimization.While these methods employ a line search strategyto achieve global convergence, the method proposed in this paperuses a trust region strategy.We establish global and superlinear convergence of the methodunder appropriate assumptions.