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Themelis, A. and Patrinos, P. (2020) Douglas-Rachford Splitting and ADMM for Nonconvex Optimization: Tight Convergence Results. SIAM Journal on Optimization, 30, 149-181.
https://doi.org/10.1137/18m1163993

has been cited by the following article:

• TITLE: A Note on the Backward-Douglas-Rachford Splitting Method for Generalized DC Programming

  AUTHORS: Xinyi Zhu, Zidan Wang

  KEYWORDS: Backward-Douglas-Rachford Splitting Method, DC Programming, Nonconvex Optimization, Step Size Result

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.14 No.4, April 23, 2026

  ABSTRACT: We revisit the Backward-Douglas-Rachford algorithm proposed by Pham et al. for solving generalized DC programming problems composed of differentiable, lower semicontinuous, and convex functions. By employing the convergence analysis framework of Themelis et al., based on the lower bound of smooth functions, and under the same standard assumptions and conditions, we recharacterize the range of the step size. Compared with the result of Pham et al., we obtain a larger step size range and simplify its expression. Moreover, under this step size condition, we prove that the sequence generated by the algorithm possesses subsequential convergence.