A SEQUENTIAL COMPLETE INERTIAL BREGMAN ADMM FOR MULTI-BLOCK NONCONVEX PROBLEMS

Lina Xia; Yujie Zhang; Hongwei Li

doi:10.11948/20250166

2026 Volume 16 Issue 5

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Lina Xia, Yujie Zhang, Hongwei Li. A SEQUENTIAL COMPLETE INERTIAL BREGMAN ADMM FOR MULTI-BLOCK NONCONVEX PROBLEMS[J]. Journal of Applied Analysis & Computation, 2026, 16(5): 2366-2391. doi: 10.11948/20250166

Citation:

Lina Xia, Yujie Zhang, Hongwei Li. A SEQUENTIAL COMPLETE INERTIAL BREGMAN ADMM FOR MULTI-BLOCK NONCONVEX PROBLEMS[J]. Journal of Applied Analysis & Computation, 2026, 16(5): 2366-2391. doi: 10.11948/20250166

A SEQUENTIAL COMPLETE INERTIAL BREGMAN ADMM FOR MULTI-BLOCK NONCONVEX PROBLEMS

1.
School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China

Author Bio: Email: xln@cug.edu.cn(L. Xia); Email: zhangyujie@cug.edu.cn(Y. Zhang)
Corresponding author: Email: hwli@cug.edu.cn(H. Li)
Fund Project: The authors were supported by National Natural Science Foundation of China (42374174)

Abstract

Abstract

In this paper, a sequential complete inertial Bregman alternating direction method of multipliers (SCIB-ADMM) is proposed for multi-block nonconvex problems. The iterative method is established by utilizing the inertial strategy and Bregman distance to enhance its processing speed and efficiency. At each iteration, the SCIB-ADMM method utilizes two different relaxation factors and updates the Lagrange multiplier twice. The convergence of the SCIB-ADMM can be established under appropriate assumptions. Moreover, numerical experiments are presented on smoothly clipped absolute deviation (SCAD) and robust principal component analysis (PCA) problems to show the effectiveness of the SCIB-ADMM method.
- Multi-block nonconvex problems /
- inertial strategy /
- Bregman distance /
- alternating direction method of multipliers /
- global convergence
MSC: 90C25

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References

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