Block coordinate proximal gradient methods with variable Bregman functions for nonsmooth separable optimization

• 成果类型: Article
• 署名作者: Hua, Xiaoqin; Yamashita, Nobuo
• 署名单位: Jiangsu University of Science & Technology; Kyoto University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-015-0969-z
• 发表日期: 2016
• 页码: 1-32
• 关键词: descent method; CONVERGENCE; algorithms; Lasso

摘要

In this paper, we propose a class of block coordinate proximal gradient (BCPG) methods for solving large-scale nonsmooth separable optimization problems. The proposed BCPG methods are based on the Bregman functions, which may vary at each iteration. These methods include many well-known optimization methods, such as the quasi-Newton method, the block coordinate descent method, and the proximal point method. For the proposed methods, we establish their global convergence properties when the blocks are selected by the Gauss-Seidel rule. Further, under some additional appropriate assumptions, we show that the convergence rate of the proposed methods is R-linear. We also present numerical results for a new BCPG method with variable kernels for a convex problem with separable simplex constraints.