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 suitable proximal parameter to each of first grouped subproblems, develop partial LQP-based Alternating Direction Method Multipliers (ADMM-LQP). The dual variable is updated twice relatively larger stepsizes than classical region (0,1+52). Using prediction-correction approach analyze properties iterates generated by ADMM-LQP, establish its global convergence sublinear rate O(1/T) in new ergodic nonergodic senses, where T denotes iteration index. We also extend algorithm nonsmooth composite similar results as our ADMM-LQP.