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

Can Yang and Yazheng Dang ()
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Can Yang: Business School, University of Shanghai for Science and Technology, Jungong Road, Shanghai 200093, China
Yazheng Dang: Business School, University of Shanghai for Science and Technology, Jungong Road, Shanghai 200093, China

Mathematics, 2025, vol. 13, issue 9, 1-22

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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