A stochastic alternating direction method of multipliers for non-smooth and non-convex optimization

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 optimization problems to solve becomes large. In this paper, we consider combining ADMM with a class of variance-reduced stochastic gradient estimators for solving large-scale non-convex and non-smooth optimization problems. Global convergence of the generated sequence is established under the additional assumption that the object function satisfies Kurdyka-Lojasiewicz property. Numerical experiments on graph-guided fused lasso and computed tomography are presented to demonstrate the performance of the proposed methods.