On the convergence rate improvement of a primal-dual splitting algorithm for solving monotone inclusion problems
On the convergence rate improvement of a primal-dual splitting algorithm for solving monotone inclusion problems
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DOI：
10.1007/s10107-014-0766-0
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发表时间：
2015-05-01
影响因子：
2.7
通讯作者：
Hendrich, Christopher
中科院分区：
文献类型：
--
作者：
Bot, Radu Ioan;Csetnek, Erno Robert;Hendrich, Christopher
为了解决单调包含问题，我们提出了基于前向后向分裂的原始-对偶分裂算法的两个改进版本(ADV Comput Math 38(3)：667-681,2013)。在对所涉及的某些算子作强单调假设下，我们得到了迭代序列分别逼近和的解的收敛阶。所研究的原始-对偶算法是完全可分解的，因为算子在每次迭代时都是单独处理的。我们还讨论了凸优化问题背景下的改进算法，并给出了聚类分析中图像处理和模式识别的数值实验。
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.