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

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• 作者：Xiaoqin Hua ; Nobuo Yamashita
• 关键词：Nonsmooth optimization ; Block coordinate proximal gradient methods ; Linear convergence ; Error bounds
• 刊名：Mathematical Programming
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：160
• 期：1-2
• 页码：1-32
• 全文大小：854 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Calculus of Variations and Optimal Control
  Mathematics of Computing
  Numerical Analysis
  Combinatorics
  Mathematical and Computational Physics
  Mathematical Methods in Physics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1436-4646
• 卷排序：160

文摘

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.