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

被引:54
作者
Bot, Radu Ioan [1 ]
Csetnek, Erno Robert [1 ]
Heinrich, Andre [2 ]
Hendrich, Christopher [2 ]
机构
[1] Univ Vienna, Fac Math, A-1090 Vienna, Austria
[2] Tech Univ Chemnitz, Dept Math, D-09107 Chemnitz, Germany
关键词
Maximally monotone operator; Strongly monotone operator; Resolvent; Operator splitting; Subdifferential; Strongly convex function; Convex optimization algorithm; Duality; MINIMIZATION; COMPOSITE;
D O I
10.1007/s10107-014-0766-0
中图分类号
TP31 [计算机软件];
学科分类号
081202 ; 0835 ;
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.
引用
收藏
页码:251 / 279
页数:29
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