2015/06/04 by Pontus Giselsson, Giselsson, Pontus · 4 citations
Computer Science · Medicine · #Complexity and Algorithms in Graphs #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Pediatric Hepatobiliary Diseases and Treatments
paper · pdf · doi:10.48550/arxiv.1506.01556
openalex publication_date 2015/06/04 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
Recently, several authors have shown local and global convergence rate\nresults for Douglas-Rachford splitting under strong monotonicity, Lipschitz\ncontinuity, and cocoercivity assumptions. Most of these focus on the convex\noptimization setting. In the more general monotone inclusion setting, Lions and\nMercier showed a linear convergence rate bound under the assumption that one of\nthe two operators is strongly monotone and Lipschitz continuous. We show that\nthis bound is not tight, meaning that no problem from the considered class\nconverges exactly with that rate. In this paper, we present tight global linear\nconvergence rate bounds for that class of problems. We also provide tight\nlinear convergence rate bounds under the assumptions that one of the operators\nis strongly monotone and cocoercive, and that one of the operators is strongly\nmonotone and the other is cocoercive. All our linear convergence results are\nobtained by proving the stronger property that the Douglas-Rachford operator is\ncontractive.\n