An Inertial Alternating Direction Method of Multipliers for Solving a Two-Block Separable Convex Minimization Problem
Received:March 12, 2020  Revised:September 27, 2020
Key Words: alternating direction method of multipliers   inertial method   Douglas-Rachford splitting algorithm  
Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.12061045; 12061046; 11661056; 11771198; 11771347; 91730306; 41390454; 11401293), the China Postdoctoral Science Foundation (Grant No.2015M571989) and the Jiangxi Province Postdoctoral Science Foundation (Grant No.2015KY51).
Author NameAffiliation
Yang YANG Department of Mathematics, Nanchang University, Jiangxi 330031, P. R. China 
Yuchao TANG Department of Mathematics, Nanchang University, Jiangxi 330031, P. R. China 
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      The alternating direction method of multipliers (ADMM) is a widely used method for solving many convex minimization models arising in signal and image processing. In this paper, we propose an inertial ADMM for solving a two-block separable convex minimization problem with linear equality constraints. This algorithm is obtained by making use of the inertial Douglas-Rachford splitting algorithm to the corresponding dual of the primal problem. We study the convergence analysis of the proposed algorithm in infinite-dimensional Hilbert spaces. Furthermore, we apply the proposed algorithm on the robust principal component analysis problem and also compare it with other state-of-the-art algorithms. Numerical results demonstrate the advantage of the proposed algorithm.
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