Proximal-Based Pre-correction Decomposition Methods for Structured Convex Minimization Problems

This paper presents two proximal-based pre-correction decomposition methods for convex minimization problems with separable structures. The methods, derived from Chen and Teboulle’s proximal-based decomposition method and He’s parallel splitting augmented Lagrangian method, remain the nice convergence property of the proximal point method and could compute variables in parallel like He’s method under the prediction-correction framework. Convergence results are established without additional assumptions. And the efficiency of the proposed methods is illustrated by some preliminary numerical experiments.