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A note on the Douglas–Rachford splitting method for optimization problems involving hypoconvex functions

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Abstract

Recently, the convergence of the Douglas–Rachford splitting method (DRSM) was established for minimizing the sum of a nonsmooth strongly convex function and a nonsmooth hypoconvex function under the assumption that the strong convexity constant \(\beta \) is larger than the hypoconvexity constant \(\omega \). Such an assumption, implying the strong convexity of the objective function, precludes many interesting applications. In this paper, we prove the convergence of the DRSM for the case \(\beta =\omega \), under relatively mild assumptions compared with some existing work in the literature.

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Author information

Authors and Affiliations

  1. School of Mathematics and Information, China West Normal University, Nanchong, 637002, Sichuan, China

    Ke Guo

  2. School of Mathematical Sciences and Key Laboratory for NSLSCS of Jiangsu Province, Nanjing Normal University, Nanjing, 210023, Jiangsu, China

    Deren Han

Authors
  1. Ke Guo
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  2. Deren Han
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Corresponding author

Correspondence to Deren Han.

Additional information

K. Guo was supported by the Natural Science Foundation of China (Grant No. 11571178), Fundamental Research Funds of China West Normal University (Grant No. 412698). D. Han was supported by a project funded by PAPD of Jiangsu Higher Education Institutions and the Natural Science Foundation of China (Grant Nos. 11625105, 11371197 and 11431002).

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Guo, K., Han, D. A note on the Douglas–Rachford splitting method for optimization problems involving hypoconvex functions. J Glob Optim 72, 431–441 (2018). https://doi.org/10.1007/s10898-018-0660-z

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  • DOI: https://doi.org/10.1007/s10898-018-0660-z

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