A proximal Peaceman–Rachford splitting method for solving the multi-block separable convex minimization problems

2018 ◽  
Vol 96 (4) ◽  
pp. 708-728 ◽  
Author(s):  
Zhongming Wu ◽  
Foxiang Liu ◽  
Min Li
Keyword(s):  
Splitting Method ◽  
Convex Minimization ◽  
Minimization Problems ◽  
Convex Minimization Problems ◽  
Separable Convex Minimization

scholarly journals A Convergent 3-Block Semi-Proximal ADMM for Convex Minimization Problems with One Strongly Convex Block

2015 ◽  
Vol 32 (04) ◽  
pp. 1550024 ◽  
Author(s):  
Min Li ◽  
Defeng Sun ◽  
Kim-Chuan Toh
Keyword(s):  
Linear Equation ◽  
Step Length ◽  
Convex Minimization ◽  
Linear Operators ◽  
Strongly Convex ◽  
Minimization Problems ◽  
Alternating Direction ◽  
Convex Minimization Problems ◽  
Separable Convex Minimization ◽  
Equation Constraint

In this paper, we present a semi-proximal alternating direction method of multipliers (sPADMM) for solving 3-block separable convex minimization problems with the second block in the objective being a strongly convex function and one coupled linear equation constraint. By choosing the semi-proximal terms properly, we establish the global convergence of the proposed sPADMM for the step-length [Formula: see text] and the penalty parameter σ ∈ (0, +∞). In particular, if σ > 0 is smaller than a certain threshold and the first and third linear operators in the linear equation constraint are injective, then all the three added semi-proximal terms can be dropped and consequently, the convergent 3-block sPADMM reduces to the directly extended 3-block ADMM with [Formula: see text].

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.

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