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Mathematics
Volume 13
Issue 9
10.3390/math13091510
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Article

Partially Symmetric Regularized Two-Step Inertial Alternating Direction Method of Multipliers for Non-Convex Split Feasibility Problems

by
Can Yang
and
Yazheng Dang
*
Business School, University of Shanghai for Science and Technology, Jungong Road, Shanghai 200093, China
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(9), 1510; https://doi.org/10.3390/math13091510 (registering DOI)
Submission received: 21 March 2025 / Revised: 18 April 2025 / Accepted: 28 April 2025 / Published: 4 May 2025
Versions Notes

Abstract

This paper presents a partially symmetric regularized two-step inertial alternating direction method of multipliers for solving non-convex split feasibility problems (SFP), which adds a two-step inertial effect to each subproblem and includes an intermediate update term for multipliers during the iteration process. Under suitable assumptions, the global convergence is demonstrated. Additionally, with the help of the Kurdyka−Łojasiewicz (KL) property, which quantifies the behavior of a function near its critical points, the strong convergence of the proposed algorithm is guaranteed. Numerical experiments are performed to demonstrate the efficacy.
Keywords: non-convex split feasibility problems; alternating direction method of multipliers; Kurdyka−Łojasiewicz (KL) property; convergence analysis; two-step inertial effect non-convex split feasibility problems; alternating direction method of multipliers; Kurdyka−Łojasiewicz (KL) property; convergence analysis; two-step inertial effect

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MDPI and ACS Style

Yang, C.; Dang, Y. Partially Symmetric Regularized Two-Step Inertial Alternating Direction Method of Multipliers for Non-Convex Split Feasibility Problems. Mathematics 2025, 13, 1510. https://doi.org/10.3390/math13091510

AMA Style

Yang C, Dang Y. Partially Symmetric Regularized Two-Step Inertial Alternating Direction Method of Multipliers for Non-Convex Split Feasibility Problems. Mathematics. 2025; 13(9):1510. https://doi.org/10.3390/math13091510

Chicago/Turabian Style

Yang, Can, and Yazheng Dang. 2025. "Partially Symmetric Regularized Two-Step Inertial Alternating Direction Method of Multipliers for Non-Convex Split Feasibility Problems" Mathematics 13, no. 9: 1510. https://doi.org/10.3390/math13091510

APA Style

Yang, C., & Dang, Y. (2025). Partially Symmetric Regularized Two-Step Inertial Alternating Direction Method of Multipliers for Non-Convex Split Feasibility Problems. Mathematics, 13(9), 1510. https://doi.org/10.3390/math13091510

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