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| Alternating direction method (ADM) has been well studied in the context of linearly constrained convex programming problems.
In the last few years, we have witnessed a number of novel applications arising from image processing, compressive sensing and statistics, etc., where the ADM approach is surprisingly efficient. In common applications of the ADM, both the objective function and the constraints are separable into two parts. Recently, the ADM has been extended to the case where the number of separable parts is a finite number. However, in each iteration, the subproblems are required to be solved exactly. In this paper, by using some reasonable inexactness criteria, we propose two inexact alternating direction based contraction methods, which substantially broaden the applicable scope of the ADM. |
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| Keywords:alternating direction method;linearly constrained convex programming;separable structure;contraction method |
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