Iteration complexity analysis of a partial LQP-based alternating direction method of multipliers
| Autor: | Bai, Jianchao, Ma, Yuxue, Sun, Hao, Zhang, Miao |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $(0,\frac{1+\sqrt{5}}{2})$. 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. Comment: 22 pages |
| Databáze: | arXiv |
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