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Volume 12
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10.3390/math12050675
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Article

An Inertial Parametric Douglas–Rachford Splitting Method for Nonconvex Problems

by
Tianle Lu
and
Xue Zhang
*
School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan 030031, China
*
Author to whom correspondence should be addressed.
Mathematics 2024, 12(5), 675; https://doi.org/10.3390/math12050675
Submission received: 22 January 2024 / Revised: 22 February 2024 / Accepted: 23 February 2024 / Published: 25 February 2024
(This article belongs to the Section E: Applied Mathematics)
Versions Notes

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 nonconvex; Douglas–Rachford splitting; inertial; parameterized

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MDPI and ACS Style

Lu, T.; Zhang, X. An Inertial Parametric Douglas–Rachford Splitting Method for Nonconvex Problems. Mathematics 2024, 12, 675. https://doi.org/10.3390/math12050675

AMA Style

Lu T, Zhang X. An Inertial Parametric Douglas–Rachford Splitting Method for Nonconvex Problems. Mathematics. 2024; 12(5):675. https://doi.org/10.3390/math12050675

Chicago/Turabian Style

Lu, Tianle, and Xue Zhang. 2024. "An Inertial Parametric Douglas–Rachford Splitting Method for Nonconvex Problems" Mathematics 12, no. 5: 675. https://doi.org/10.3390/math12050675

APA Style

Lu, T., & Zhang, X. (2024). An Inertial Parametric Douglas–Rachford Splitting Method for Nonconvex Problems. Mathematics, 12(5), 675. https://doi.org/10.3390/math12050675

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