Journal
APPLIED NUMERICAL MATHEMATICS
Volume 165, Issue -, Pages 500-518Publisher
ELSEVIER
DOI: 10.1016/j.apnum.2021.03.014
Keywords
Convex optimization; Alternating direction method of multipliers; Proximal term; Larger stepsize; Convergence complexity
Categories
Funding
- National Natural Science Foundation of China [12001430, 72071158]
- Fundamental Research Funds for the Central Universities [G2020KY05203]
- China Postdoctoral Science Foundation [2020M683545]
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This paper investigates a convex optimization problem with multi-block variables and separable structures. A partial LQP-based ADMM algorithm is proposed, and the convergence and convergence rate are analyzed using a prediction-correction approach.
In this paper, we consider a prototypical convex optimization problem with multi-block variables and separable structures. By adding the Logarithmic Quadratic Proximal (LQP) regularizer with suitable proximal parameter to each of the first grouped subproblems, we develop a partial LQP-based Alternating Direction Method of Multipliers (ADMM-LQP). The dual variable is updated twice with relatively larger stepsizes than the classical region (0, 1+root 5/2 ). Using a prediction-correction approach to analyze properties of the iterates generated by ADMM-LQP, we establish its global convergence and sublinear convergence rate of O(1/T) in the new ergodic and nonergodic senses, where T denotes the iteration index. We also extend the algorithm to a nonsmooth composite convex optimization and establish similar convergence results as our ADMM-LQP. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.
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