A distributed Douglas-Rachford splitting method for multi-block convex minimization problems

2015 ◽  
Vol 42 (1) ◽  
pp. 27-53 ◽  
Author(s):  
Hongjin He ◽  
Deren Han
Keyword(s):  
Splitting Method ◽  
Convex Minimization ◽  
Minimization Problems ◽  
Convex Minimization Problems

scholarly journals Novel forward–backward algorithms for optimization and applications to compressive sensing and image inpainting

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Suthep Suantai ◽  
Muhammad Aslam Noor ◽  
Kunrada Kankam ◽  
Prasit Cholamjiak
Keyword(s):  
Compressive Sensing ◽  
Splitting Method ◽  
Image Inpainting ◽  
Optimal Choice ◽  
Convex Minimization ◽  
Objective Functions ◽  
Classification Problems ◽  
Minimization Problems ◽  
Convex Minimization Problems ◽  
Continuity Assumption

AbstractThe forward–backward algorithm is a splitting method for solving convex minimization problems of the sum of two objective functions. It has a great attention in optimization due to its broad application to many disciplines, such as image and signal processing, optimal control, regression, and classification problems. In this work, we aim to introduce new forward–backward algorithms for solving both unconstrained and constrained convex minimization problems by using linesearch technique. We discuss the convergence under mild conditions that do not depend on the Lipschitz continuity assumption of the gradient. Finally, we provide some applications to solving compressive sensing and image inpainting problems. Numerical results show that the proposed algorithm is more efficient than some algorithms in the literature. We also discuss the optimal choice of parameters in algorithms via numerical experiments.

scholarly journals A primal-dual dynamical approach to structured convex minimization problems

2020 ◽  
Vol 269 (12) ◽  
pp. 10717-10757 ◽  
Author(s):  
Radu Ioan Boţ ◽  
Ernö Robert Csetnek ◽  
Szilárd Csaba László
Keyword(s):  
Convex Minimization ◽  
Minimization Problems ◽  
Dynamical Approach ◽  
Convex Minimization Problems ◽  
Primal Dual
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