An ADM-based splitting method for separable convex programming

Authors:
Deren Han;Xiaoming Yuan;Wenxing Zhang;Xingju Cai
Affiliations:
School of Mathematical Sciences and Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing, P.R. China 210023;Department of Mathematics, Hong Kong Baptist University, Hong Kong, P.R. China;Department of Mathematics, Nanjing University, Nanjing, P.R. China 210093;Department of Mathematics, Nanjing University, Nanjing, P.R. China 210093
Venue:
Computational Optimization and Applications
Year:
2013

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Abstract

We consider the convex minimization problem with linear constraints and a block-separable objective function which is represented as the sum of three functions without coupled variables. To solve this model, it is empirically effective to extend straightforwardly the alternating direction method of multipliers (ADM for short). But, the convergence of this straightforward extension of ADM is still not proved theoretically. Based on ADM's straightforward extension, this paper presents a new splitting method for the model under consideration, which is empirically competitive to the straightforward extension of ADM and meanwhile the global convergence can be proved under standard assumptions. At each iteration, the new method corrects the output of the straightforward extension of ADM by some slight correction computation to generate a new iterate. Thus, the implementation of the new method is almost as easy as that of ADM's straightforward extension. We show the numerical efficiency of the new method by some applications in the areas of image processing and statistics.