Douglas--Rachford Splitting and ADMM for Pathological Convex Optimization

摘要: Despite the vast literature on DRS and ADMM, there has been very little work analyzing their behavior under pathologies. Most analyses assume a primal solution exists, dual strong duality holds. When these assumptions are not met, i.e., pathologies, theory often breaks down empirical performance may degrade significantly. In this paper, we establish that only requires to work, in sense asymptotically iterates approximately feasible optimal.