Convergence Analysis of an Inexact Three-Operator Splitting Algorithm

Chunxiang Zong, Yuchao Tang, Yeol Cho
2018 Symmetry  
The three-operator splitting algorithm is a new splitting algorithm for finding monotone inclusion problems of the sum of three maximally monotone operators, where one is cocoercive. As the resolvent operator is not available in a closed form in the original three-operator splitting algorithm, in this paper, we introduce an inexact three-operator splitting algorithm to solve this type of monotone inclusion problem. The theoretical convergence properties of the proposed iterative algorithm are
more » ... ive algorithm are studied in general Hilbert spaces under mild conditions on the iterative parameters. As a corollary, we obtain general convergence results of the inexact forward-backward splitting algorithm and the inexact Douglas-Rachford splitting algorithm, which extend the existing results in the literature.
doi:10.3390/sym10110563 fatcat:pdjwjidscnagna6tqqc4std2vm