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This paper considers the convex minimization problem with linear constraints and a separable objective function which is the sum of many individual functions without coupled variables. An algorithm is developed by splitting the augmented Lagrangian function in a parallel way. The new algorithm differs substantially from existing splitting methods in alternating style which require solving the decomposed subproblems sequentially, while it remains the main superiority of existing splitting methods in that the resulting subproblems could be simple enough to have closed-form solutions for such an application whose functions in the objective are simple. We show applicability and encouraging efficiency of the new algorithm by some applications in image processing.

An augmented Lagrangian based parallel splitting method for separable convex minimization with applications to image processing