A class of decomposition methods for convex optimization and monotone variational inclusions via the hybrid inexact proximal point framework

We show that the decomposition method for convex programming proposed by Chen and Teboulle can be regarded as a special case in the hybrid inexact proximal point framework. We further demonstrate that the more general decomposition algorithms for variational inequalities introduced by Tseng are also either a special case in this framework or very closely related to it. This analysis provides a new insight into the nature of those decomposition schemes, as well as paves the way for deriving more practical methods by solving subproblems approximately (for example, using appropriate bundle methods). As a by-product, we also improve some convergence results and extend the approach to a more general class of problems.

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