Inexact Operator Splitting Method for Monotone Inclusion Problems

The Douglas-Peaceman-Rachford-Varga operator splitting methods are a class of efficient methods for finding a zero of the sum of two maximal monotone operators in a real Hilbert space; however, they are sometimes difficult or even impossible to solve the subproblems exactly. In this paper, we suggest an inexact version in which some relative error criterion is discussed. The corresponding convergence properties are established, and some preliminary numerical experiments are reported to illustrate its efficiency.