Bregman Three-Operator Splitting Methods
本文提出了使用广义Bregman距离的原始对偶近端分裂方法，扩展了Condat–Vũ和PD3O算法，并给出了收敛分析，对求解凸优化问题的研究者有用。
Abstract 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–Vũ algorithms and the primal–dual three-operator (PD3O) algorithm. The Bregman extensions of the Condat–Vũ 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–Vũ algorithm applied to equality-constrained problems. Finally, we propose a Bregman extension of PD3O and analyze its convergence.