Three-operator splitting algorithm for a class of variational inclusion problems

被引：0
作者：
Dang Van Hieu
Le Van Vy
Pham Kim Quy
机构：
[1] Ton Duc Thang University,Applied Analysis Research Group, Faculty of Mathematics and Statistics
[2] College of Air Force,Department of Mathematics
来源：
Bulletin of the Iranian Mathematical Society | 2020年 / 46卷
关键词：
Forward–backward method; Tseng’s method; Operator splitting method; 65J15; 47H05; 47J25; 47J20; 91B50;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper concerns with a new three-operator splitting algorithm for solving a class of variational inclusions. The main advantage of the proposed algorithm is that it can be easily implemented without the prior knowledge of Lipschitz constant, strongly monotone constant and cocoercive constant of component operators. A reason explained for this is that the algorithm uses a sequence of stepsizes which is diminishing and non-summable. The strong convergence of the algorithm is established. Several fundamental numerical experiments are given to illustrate the behavior of the new algorithm and compare it with other algorithms.
引用
收藏
页码：1055 / 1071
页数：16
相关论文
共 33 条
[1]  
Attouch H(2018)Backward–forward algorithms for structured monotone inclusions in Hilbert spaces J. Math. Anal. Appl. 457 1095-1117
[2]  
Peypouquet J(2005)Signal recovery by proximal forward–backward splitting SIAM Multiscale Model. Simul. 4 1168-1200
[3]  
Redont P(2004)An iterative thresholding algorithm for linear inverse problems with a sparsity constraint Commun. Pure Appl. Math. 57 1413-1457
[4]  
Combettes PL(2017)A three-operator splitting scheme and its optimization applications Set Valued Var. Anal. 25 829-858
[5]  
Wajs V(2010)A family of operator splitting methods revisited Nonlinear Anal. 72 4307-4315
[6]  
Daubechies I(2009)Efficient online and batch learning using forward–backward splitting J. Mach. Learn. Res. 10 2899-2934
[7]  
Defrise M(2018)New extragradient—like algorithms for strongly pseudomonotone variational inequalities J. Glob. Optim. 70 385-399
[8]  
De Mol C(2018)Convergence analysis of a new algorithm for strongly pseudomontone equilibrium problems Numer. Algor. 77 983-1001
[9]  
Davis D(2018)New extragradient method for a class of equilibrium problems in Hilbert spaces Appl. Anal. 97 811-824
[10]  
Yin WT(2019)An explicit parallel algorithm for variational inequalities Bull. Malaysian Math. Soc. 42 201-221
1234