scholarly journals Correction to: A partially isochronous splitting algorithm for three-block separable convex minimization problems

2018 ◽  
Vol 44 (4) ◽  
pp. 1117-1118
Author(s):  
Hongjin He ◽  
Liusheng Hou ◽  
Hong-Kun Xu
Keyword(s):  
Convex Minimization ◽  
Splitting Algorithm ◽  
Minimization Problems ◽  
Convex Minimization Problems ◽  
Separable Convex Minimization

scholarly journals An accelerated viscosity forward-backward splitting algorithm with the linesearch process for convex minimization problems

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Suthep Suantai ◽  
Pachara Jailoka ◽  
Adisak Hanjing
Keyword(s):  
Lipschitz Constant ◽  
Optimization Methods ◽  
Convergence Result ◽  
Convex Minimization ◽  
Signal Recovery ◽  
Splitting Algorithm ◽  
Minimization Problems ◽  
Convex Minimization Problems ◽  
Continuity Assumption ◽  
Inertial Technique

AbstractIn this paper, we consider and investigate a convex minimization problem of the sum of two convex functions in a Hilbert space. The forward-backward splitting algorithm is one of the popular optimization methods for approximating a minimizer of the function; however, the stepsize of this algorithm depends on the Lipschitz constant of the gradient of the function, which is not an easy work to find in general practice. By using a new modification of the linesearches of Cruz and Nghia [Optim. Methods Softw. 31:1209–1238, 2016] and Kankam et al. [Math. Methods Appl. Sci. 42:1352–1362, 2019] and an inertial technique, we introduce an accelerated viscosity-type algorithm without any Lipschitz continuity assumption on the gradient. A strong convergence result of the proposed algorithm is established under some control conditions. As applications, we apply our algorithm to solving image and signal recovery problems. Numerical experiments show that our method has a higher efficiency than the well-known methods in the literature.

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].

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