Pontus Gisselson, Lund University

Abstract

Several local and global linear convergence rate results for the alternating direction method of multipliers (ADMM) have appeared in the literature over the last couple of years. Many of these are derived under strong monotonicity, Lipschitz continuity, and/or cocoercivity assumptions, and focus on the convex optimization setting. It is well known that ADMM is obtained by applying the Douglas-Rachford algorithm

to a Fenchel dual problem. In this talk, we show that the linear convergence results for ADMM follow from that the Douglas-Rachford operator is contractive under the stated assumptions. The benefits of our analysis are that 1) the contraction factors are sharp 2) the proofs are fairly simple, based on operator theoretic analysis.

Slides     Video