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Douglas–Rachford splitting and ADMM for pathological convex optimization

Author

Listed:
  • Ernest K. Ryu

    (UCLA)

  • Yanli Liu

    (UCLA)

  • Wotao Yin

    (UCLA)

Abstract

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.

Suggested Citation

  • Ernest K. Ryu & Yanli Liu & Wotao Yin, 2019. "Douglas–Rachford splitting and ADMM for pathological convex optimization," Computational Optimization and Applications, Springer, vol. 74(3), pages 747-778, December.
    • Handle: RePEc:spr:coopap:v:74:y:2019:i:3:d:10.1007_s10589-019-00130-9
    DOI: 10.1007/s10589-019-00130-9
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    References listed on IDEAS

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