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DOI: 10.23952/jnfa.2024.34
Received November 3, 2024; Accepted December 1, 2024; Published December 31, 2024
Abstract. The class of generalized DC (difference-of-convex functions) programming is the problem of minimizing the sum of two convex functions minus a smooth and convex function. A unified Douglas-Rachford splitting algorithm was investigated to solve this class of problems in the literature and shown to converge to a critical point of the problem with promising numerical performance. In this paper, we devise a new variation of the unified Douglas-Rachford splitting algorithm, a unified Douglas-Rachford splitting algorithm with momentum, to solve generalized DC programming in Hilbert spaces. We show that the iterative sequence generated by our algorithm converges weakly to a critical point of the generalized DC programming. Numerical experiments demonstrate versatility and effectiveness of our algorithm over the original unified Douglas-Rachford splitting algorithm and other versions investigated recently in the literature.
How to Cite this Article:
Y. Gong, T. Li, Y. Shehu, Z. Yang, The Douglas-Rachford splitting algorithm with momentum for generalized DC programming, J. Nonlinear Funct. Anal. 2024 (2024) 34.