非凸非光滑优化问题的惯性Bregman ADMM的收敛性分析  

Convergence of Build-in Inertial Bregman ADMM for Nonsmooth Nonconvex Optimization

作　　者：魏娇 罗洪林 WEI Jiao;LUO Honglin(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2022年第5期14-23,共10页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11991024,No.11771064);重庆市高校创新研究群体项目(No.20A110029)。

摘　　要：【目的】针对具有可分结构的非凸非光滑优化问题,提出一种内置惯性Bregman交替方向乘子法。【方法】为了加快算法的收敛速度,在Bregman交替方向乘子法的框架下,对子问题中的Bregman度量内置惯性项。【结果】在生成的点列有界的条件下,利用Kurdyka-Lojasiewicz性质,证明了算法的渐进收敛性。【结论】数值实验结果表明了该算法的有效性。[Purposes]A class of linearly constrained nonconvex nonsmooth optimization problems with separable structures is considered. a new Bregman ADMM with build-in inertial force is proposed for solving such nonconvex nonsmooth optimization problems. [Methods]In order to accelerate the convergence speed of the algorithm, in the framework of the Bregman Multiplier lalternating direction method, the built-in inertia term of Bregman metric in the subproblem. [Findings]It proves that the iterative sequence generated by the algorithm converges asymptotically to a critical point of the problem under some mild assumptions. [Conclusions]Some preliminary numerical results on solving a nonconvex matrix decomposition problem with a low-rank term and a sparse term to illustrate the efficiency of the proposed method.

关 键 词：具有可分结构的非凸非光滑优化 内置惯性Bregman交替方向乘子法 Kurdyka-Lojasiewicz性质 渐进收敛性 

分 类 号：O221.2[理学—运筹学与控制论]