Relaxed inertial proximal Peaceman-Rachford splitting method for separable convex programming

作     者：Yongguang HE Huiyun LI Xinwei LIU 

作者机构：Institute of Mathematics Hebei University of Technology Tianjin 300401 China School of Control Science and Engineering Hebei University of Technology Tianjin 300401 China 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2018年第13卷第3期

页      面：555-578页

核心收录：

学科分类：07[理学] 08[工学] 0817[工学-化学工程与技术] 081701[工学-化学工程] 0712[理学-科学技术史(分学科，可授理学、工学、农学、医学学位)] 0701[理学-数学] 

基　　金：Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant Nos. 11671116  11271107  91630202） and the Natural Science Foundation of Hebei Province of China （No. A2015202365）. 

主　　题：Convex programming inertial proximal Peaceman-Rachford splitting method relaxation factor global convergence 

摘      要：The strictly contractive Peaceman-Rachford splitting method is one of effective methods for solving separable convex optimization problem, and the inertial proximal Peaceman-Rachford splitting method is one of its important variants. It is known that the convergence of the inertial proximal Peaceman- Rachford splitting method can be ensured if the relaxation factor in Lagrangian multiplier updates is underdetermined, which means that the steps for the Lagrangian multiplier updates are shrunk conservatively. Although small steps play an important role in ensuring convergence, they should be strongly avoided in practice. In this article, we propose a relaxed inertial proximal Peaceman- Rachford splitting method, which has a larger feasible set for the relaxation factor. Thus, our method provides the possibility to admit larger steps in the Lagrangian multiplier updates. We establish the global convergence of the proposed algorithm under the same conditions as the inertial proximal Peaceman-Rachford splitting method. Numerical experimental results on a sparse signal recovery problem in compressive sensing and a total variation based image denoising problem demonstrate the effectiveness of our method.