Computational Optimization and Applications

, Volume 74, Issue 3, pp 747–778 | Cite as

Douglas–Rachford splitting and ADMM for pathological convex optimization

  • Ernest K. RyuEmail author
  • Yanli Liu
  • Wotao Yin


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.


Douglas–Rachford splitting Strong duality Pathological convex programs 

Mathematics Subject Classification

90C46 49N15 90C25 



Funding was provided by Division of Mathematical Sciences (DMS-1720237), Office of Naval Research Global (N000141712162).


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Authors and Affiliations

  1. 1.UCLALos AngelesUSA

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