On the convergence rate improvement of a primal-dual splitting algorithm for solving monotone inclusion problems

• 成果类型: Article
• 署名作者: Bot, Radu Ioan; Csetnek, Erno Robert; Heinrich, Andre; Hendrich, Christopher
• 署名单位: University of Vienna; Technische Universitat Chemnitz
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-014-0766-0
• 发表日期: 2015
• 页码: 251-279
• 关键词: minimization; composite

摘要

We present two modified versions of the primal-dual splitting algorithm relying on forward-backward splitting proposed in V (Adv Comput Math 38(3):667-681, 2013) for solving monotone inclusion problems. Under strong monotonicity assumptions for some of the operators involved we obtain for the sequences of iterates that approach the solution orders of convergence of and , for , respectively. The investigated primal-dual algorithms are fully decomposable, in the sense that the operators are processed individually at each iteration. We also discuss the modified algorithms in the context of convex optimization problems and present numerical experiments in image processing and pattern recognition in cluster analysis.