Abstract:

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.

Key words: Structured convex programming ,  Parallel splitting ,  Proximal
point method , Augmented Lagrangian , Prediction-correction method