Iteration complexity analysis of a partial LQP-based alternating direction method of multipliers.

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 + 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. [ABSTRACT FROM AUTHOR]