A Class of Variable Metric Decomposition Methods for Monotone Variational Inclusions

作者：Lotito P A^*; Parente L A; Solodov M V

来源：Journal of Convex Analysis, 2009, 16(3-4): 857-880.

• Proximal point methods
• variable metric
• maximal monotone operator
• variational inclusion
• splitting
• decomposition

We extend the general decomposition scheme of [32], which is based on the hybrid inexact proximal point method of [38], to allow the use of variable metric in subproblems, along the Lines of [23]. We show that the new general scheme includes as special cases the splitting method for composite mappings [25] and the proximal alternating directions method [13, 17] (in addition to the decomposition methods of [10, 42] that were already covered by [32]). Apart from giving a unified insight into the decomposition methods in question and openning the possibility of using variable metric, which is a computationally important issue, this development also provides linear rate of convergence results not previously available for splitting of composite mappings and for the proximal alternating directions methods.

• 出版日期2009