A customized proximal point algorithm for convex minimization with linear constraints

Abstract

This paper demonstrates a customized application of the classical proximal point algorithm (PPA) to the convex minimization problem with linear constraints. We show that if the proximal parameter in metric form is chosen appropriately, the application of PPA could be effective to exploit the simplicity of the objective function. The resulting subproblems could be easier than those of the augmented Lagrangian method (ALM), a benchmark method for the model under our consideration. The efficiency of the customized application of PPA is demonstrated by some image processing problems.