  Alternating direction method of multipliers (ADMM) is a popular first-order
method owing to its simplicity and efficiency. However, similar to other
proximal splitting methods, the performance of ADMM degrades significantly when
the scale of the optimization problems to solve becomes large. In this paper,
we consider combining ADMM with a class of stochastic gradient with variance
reduction for solving large-scale non-convex and non-smooth optimization
problems. Global convergence of the generated sequence is established under the
extra additional assumption that the object function satisfies
Kurdyka-Lojasiewicz (KL) property. Numerical experiments on graph-guided fused
Lasso and computed tomography are presented to demonstrate the performance of
the proposed methods.
