Partial symmetric regularized alternating direction method of multipliers for non-convex split feasibility problems

Yue Zhao; Meixia Li; Xiaowei Pan; Jingjing Tan; Yue Zhao; Meixia Li; Xiaowei Pan; Jingjing Tan

doi:10.3934/math.2025142

AIMS Mathematics

2025, Volume 10, Issue 2: 3041-3061. doi: 10.3934/math.2025142

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Research article

Partial symmetric regularized alternating direction method of multipliers for non-convex split feasibility problems

1.
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
2.
School of Mathematics and Statistics, Weifang University, Weifang 261061, China

Received: 23 December 2024 Revised: 02 February 2025 Accepted: 11 February 2025 Published: 19 February 2025
MSC : 47J20, 47J25, 47J30

In this paper, we propose a kind of partial symmetric regularized alternating direction method of multipliers for solving non-convex split feasibility problems. This algorithm adds an update to the Lagrangian multiplier term during the iteration process. Existing results about ADMM cannot be widely applied because the problem under consideration does not satisfy the assumptions usually claimed. The global convergence of the algorithm is proved under appropriate assumptions. And when the augmented Lagrangian function satisfies the KL property, the strong convergence of the algorithm is obtained. Furthermore, when the correlation function has a special structure, the sublinear and linear convergence rates of the algorithm are ensured. Finally, numerical experiments are conducted to show that the algorithm is effective.
- non-convex split feasibility problems,
- alternating direction method of multipliers,
- KL property,
- convergence rate
Citation: Yue Zhao, Meixia Li, Xiaowei Pan, Jingjing Tan. Partial symmetric regularized alternating direction method of multipliers for non-convex split feasibility problems[J]. AIMS Mathematics, 2025, 10(2): 3041-3061. doi: 10.3934/math.2025142

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Abstract

In this paper, we propose a kind of partial symmetric regularized alternating direction method of multipliers for solving non-convex split feasibility problems. This algorithm adds an update to the Lagrangian multiplier term during the iteration process. Existing results about ADMM cannot be widely applied because the problem under consideration does not satisfy the assumptions usually claimed. The global convergence of the algorithm is proved under appropriate assumptions. And when the augmented Lagrangian function satisfies the KL property, the strong convergence of the algorithm is obtained. Furthermore, when the correlation function has a special structure, the sublinear and linear convergence rates of the algorithm are ensured. Finally, numerical experiments are conducted to show that the algorithm is effective.

References

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