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Despite the vast literature on DRS and ADMM, there has been very little workanalyzing their behavior under pathologies. Most analyses assume a primalsolution exists, a dual solution exists, and strong duality holds. When theseassumptions are not met, i.e., under pathologies, the theory often breaks downand the empirical performance may degrade significantly. In this paper, weestablish that DRS only requires strong duality to work, in the sense thatasymptotically iterates are approximately feasible and approximately optimal.

Douglas--Rachford Splitting and ADMM for Pathological Convex Optimization