The alternating direction method of multipliers(ADMM for short) is efficient for linearly constrained convex optimization problem. The practical computational cost of ADMM depends on the sub-problem solvers. The proximal point algorithm is a common sub-problem-solver. However, the proximal parameter is sensitive in the proximal ADMM. In this paper, we propose a homotopy-based proximal linearized ADMM, in which a homotopy method is used to solve the sub-problems at each iteration. Under some suitable conditions, the global convergence and the convergence rate of O(1/k) in the worst case of the proposed method are proven. Some preliminary numerical results indicate the validity of the proposed method.
