A multi-step doubly stabilized bundle method for nonsmooth convex optimization

In this paper, by incorporating a multi-step scheme into the doubly stabilized bundle method (DSBM) recently developed by Oliveira and Solodov (2016), we propose a multistep doubly stabilized bundle method (MDSBM) for solving nonsmooth convex optimization problems. In contrast to a single sequence generated by DSBM, the MDSBM generates three related iteration sequences. One is used to build the cutting-planes model of the objective function, another is served as the stability centers, and the third is the sequence of solutions to our new doubly stabilized subproblems. In addition, we present a new descent test criterion, aiming to take advantage of the multi-step scheme. We establish global convergence of the proposed method, and finally present some promising numerical results. (C) 2020 Elsevier Inc. All rights reserved.