scholarly journals A Douglas--Rachford Type Primal-Dual Method for Solving Inclusions with Mixtures of Composite and Parallel-Sum Type Monotone Operators

2013 ◽  
Vol 23 (4) ◽  
pp. 2541-2565 ◽  
Author(s):  
Radu Ioan Boţ ◽  
Christopher Hendrich
Keyword(s):  
Monotone Operators ◽  
Dual Method ◽  
Parallel Sum ◽  
Primal Dual

scholarly journals Primal-Dual Splitting Algorithms for Solving Structured Monotone Inclusion with Applications

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2415
Author(s):  
Jinjian Chen ◽  
Xingyu Luo ◽  
Yuchao Tang ◽  
Qiaoli Dong
Keyword(s):  
Numerical Experiments ◽  
Monotone Operators ◽  
Simple Calculation ◽  
Monotone Inclusion ◽  
Splitting Algorithm ◽  
Splitting Algorithms ◽  
Parallel Sum ◽  
Primal Dual ◽  
Cocoercive Operator ◽  
Maximally Monotone Operators

This work proposes two different primal-dual splitting algorithms for solving structured monotone inclusion containing a cocoercive operator and the parallel-sum of maximally monotone operators. In particular, the parallel-sum is symmetry. The proposed primal-dual splitting algorithms are derived from two approaches: One is the preconditioned forward–backward splitting algorithm, and the other is the forward–backward–half-forward splitting algorithm. Both algorithms have a simple calculation framework. In particular, the single-valued operators are processed via explicit steps, while the set-valued operators are computed by their resolvents. Numerical experiments on constrained image denoising problems are presented to show the performance of the proposed algorithms.

Primal-dual method for continuous max-flow approaches

2015 ◽  
pp. 17-24 ◽  
Author(s):  
Ke Wei ◽  
Xue-Cheng Tai ◽  
Tony Chan ◽  
Shingyu Leung
Keyword(s):  
Dual Method ◽  
Primal Dual

scholarly journals Accelerated dual-averaging primal–dual method for composite convex minimization

2020 ◽  
Vol 35 (4) ◽  
pp. 741-766
Author(s):  
Conghui Tan ◽  
Yuqiu Qian ◽  
Shiqian Ma ◽  
Tong Zhang
Keyword(s):  
Convex Minimization ◽  
Dual Method ◽  
Primal Dual ◽  
Dual Averaging
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