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Douglas--Rachford Splitting and ADMM for Pathological Convex Optimization
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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, a dual solution exists, and strong duality holds. When these assumptions are not met, i.e., under pathologies, the theory often breaks down and the empirical performance may degrade significantly. In this paper, we establish that DRS only requires strong duality to work, in the sense that asymptotically iterates are approximately feasible and approximately optimal.
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Cited by 1 Pith paper
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On the behaviour of the Douglas-Rachford algorithm for minimizing a convex function subject to a linear constraint
The Douglas-Rachford algorithm converges weakly to a normal solution of minimizing a convex function over a linear subspace even when the original problem is infeasible.
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