A Proximal Alternating Direction Method of Multipliers with a Substitution Procedure

Abstract EN

In this paper, we considers the separable convex programming problem with linear constraints.

Its objective function is the sum of m individual blocks with nonoverlapping variables and each block consists of two functions: one is smooth convex and the other one is convex.

For the general case m≥3, we present a gradient-based alternating direction method of multipliers with a substitution.

For the proposed algorithm, we prove its convergence via the analytic framework of contractive-type methods and derive a worst-case O1/t convergence rate in nonergodic sense.

Finally, some preliminary numerical results are reported to support the efficiency of the proposed algorithm.