论文标题
Bregman三 - 操作员分裂方法
Bregman three-operator splitting methods
论文作者
论文摘要
本文介绍了用于凸优化的原始双二近端分裂方法，其中使用广义的布雷格曼距离来定义原始和双重近端更新步骤。该方法扩展了原始和双孔 - VU算法以及原始的双偶三个操作员（PD3O）算法。 Condat-Vu算法的Bregman扩展是从应用于单调包含问题的Bregman近端方法得出的。基于这种解释，提出了两种方法的收敛分析的统一框架。我们还引入了一个线路搜索过程，以用于将其用于公平限制问题的Bregman Dual Dual Condat-Vu算法中的步骤尺寸选择。最后，我们提出了Bregman的PD3O扩展，并分析其收敛性。
The paper presents primal-dual proximal splitting methods for convex optimization, in which generalized Bregman distances are used to define the primal and dual proximal update steps. The methods extend the primal and dual Condat-Vu algorithms and the primal-dual three-operator (PD3O) algorithm. The Bregman extensions of the Condat-Vu algorithms are derived from the Bregman proximal point method applied to a monotone inclusion problem. Based on this interpretation, a unified framework for the convergence analysis of the two methods is presented. We also introduce a line search procedure for stepsize selection in the Bregman dual Condat-Vu algorithm applied to equality-constrained problems. Finally, we propose a Bregman extension of PD3O and analyze its convergence.
