Tseng's Algorithm with Extrapolation from the past Endowed with Variable Metrics and Error Terms

被引:5
作者
Tongnoi, Buris [1 ]
机构
[1] Univ Vienna, Fac Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria
关键词
Convergence analysis; iterative methods; optimization problems; resolvent operators; Tseng's algorithm; BACKWARD SPLITTING METHOD; PROXIMAL POINT ALGORITHM; MONOTONE INCLUSIONS; CONVERGENCE;
D O I
10.1080/01630563.2022.2158196
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we propose a variable metric version of Tseng's algorithm (the forward-backward-forward algorithm: FBF) combined with extrapolation from the past that includes error terms for finding a zero of the sum of a maximally monotone operator and a monotone Lipschitzian operator in Hilbert spaces. The algorithm, which is a modified forward-reflected-backword method, is endowed with variable metrics and error terms. Primal-dual algorithms are also proposed for monotone inclusion problems involving compositions with linear operators. The primal-dual problem occurring in image deblurring demonstrates an application of our theoretical results.
引用
收藏
页码:87 / 123
页数:37
相关论文
共 36 条
[1]  
[Anonymous], 2001, Studies in Computational Mathematics
[2]   A splitting algorithm for dual monotone inclusions involving cocoercive operators [J].
Bang Cong Vu .
ADVANCES IN COMPUTATIONAL MATHEMATICS, 2013, 38 (03) :667-681
[3]  
Bauschke HH, 2011, CMS BOOKS MATH, P1, DOI 10.1007/978-1-4419-9467-7
[4]   A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems [J].
Beck, Amir ;
Teboulle, Marc .
SIAM JOURNAL ON IMAGING SCIENCES, 2009, 2 (01) :183-202
[5]  
Becker S., 2012, ADV NEURAL INFORM PR, P25
[6]   The ordered subsets mirror descent optimization method with applications to tomography [J].
Ben-Tal, A ;
Margalit, T ;
Nemirovski, A .
SIAM JOURNAL ON OPTIMIZATION, 2001, 12 (01) :79-108
[7]   Two Steps at a Time-Taking GAN Training in Stride with Tseng?s Method [J].
Bohm, Axel ;
Sedlmayer, Michael ;
Csetnek, Erno Robert ;
Bot, Radu Ioan .
SIAM JOURNAL ON MATHEMATICS OF DATA SCIENCE, 2022, 4 (02) :750-771
[8]  
Bot R.I., 2010, Conjugate Duality in Convex Optimization, V637
[9]   On the convergence rate of a forward-backward type primal-dual splitting algorithm for convex optimization problems [J].
Bot, Radu Ioan ;
Csetnek, Ernoe Robert .
OPTIMIZATION, 2015, 64 (01) :5-23
[10]   A MONOTONE plus SKEW SPLITTING MODEL FOR COMPOSITE MONOTONE INCLUSIONS IN DUALITY [J].
Briceno-Arias, Luis M. ;
Combettes, Patrick L. .
SIAM JOURNAL ON OPTIMIZATION, 2011, 21 (04) :1230-1250