Inexact Alternating Direction Methods of Multipliers with Logarithmic-Quadratic Proximal Regularization

In the literature, it was shown recently that the Douglas-Rachford alternating direction method of multipliers can be combined with the logarithmic-quadratic proximal regularization for solving a class of variational inequalities with separable structures. This paper studies the inexact version of this combination, where the resulting subproblems are allowed to be solved approximately subject to different inexactness criteria. We prove the global convergence and establish worst-case convergence rates for the derived inexact algorithms.