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Douglas--Rachford Splitting and ADMM for Pathological Convex Optimization

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arxiv 1801.06618 v3 pith:3SVOGOWQ submitted 2018-01-20 math.OC

classification math.OC
keywords admmapproximatelydualityexistspathologiessolutionstrongunder
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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

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the behaviour of the Douglas-Rachford algorithm for minimizing a convex function subject to a linear constraint

    math.OC 2019-08 accept novelty 7.0 of 10

    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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