An Inertial Parametric Douglas–Rachford Splitting Method for Nonconvex Problems

Tianle Lu and Xue Zhang ()
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Tianle Lu: School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan 030031, China
Xue Zhang: School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan 030031, China

Mathematics, 2024, vol. 12, issue 5, 1-24

Abstract: In this paper, we propose an inertial parametric Douglas–Rachford splitting method for minimizing the sum of two nonconvex functions, which has a wide range of applications. The proposed algorithm combines the inertial technique, the parametric technique, and the Douglas–Rachford method. Subsequently, in theoretical analysis, we construct a new merit function and establish the convergence of the sequence generated by the inertial parametric Douglas–Rachford splitting method. Finally, we present some numerical results on nonconvex feasibility problems to illustrate the efficiency of the proposed method.

Keywords: nonconvex; Douglas–Rachford splitting; inertial; parameterized (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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