A relaxation-type accelerating iteration method for large sparse horizontal nonlinear complementarity problems

Liwei Tian; Suping Liu; Hua Zheng; Xiaoping Lu; Liwei Tian; Suping Liu; Hua Zheng; Xiaoping Lu

doi:10.3934/era.2025328

Electronic Research Archive

2025, Volume 33, Issue 12: 7442-7462. doi: 10.3934/era.2025328

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Research article

A relaxation-type accelerating iteration method for large sparse horizontal nonlinear complementarity problems

1.
School of Computer Science, Guangdong University of Science and Technology, Dongguan 523083, China
2.
School of Mathematics and Statistics, Shaoguan University, Shaoguan 512005, China
3.
School of Computer Science and Engineering, Macau University of Science and Technology, Macao, China

Received: 13 September 2025 Revised: 06 November 2025 Accepted: 04 December 2025 Published: 10 December 2025

In this work, a relaxation modulus-based matrix splitting iteration method for large sparse horizontal nonlinear complementarity problems was established. The convergence analysis was presented, where the proposed conditions were shown to be weaker than the existing result. Furthermore, a practical selection strategy of the relaxation parameter was provided by analyzing the error function in each iteration. Numerical examples were given to verify the theoretical improvement and show the effectiveness of the proposed method with the suggested relaxation parameters.
- horizontal nonlinear complementarity problem,
- modulus-based method,
- relaxation
Citation: Liwei Tian, Suping Liu, Hua Zheng, Xiaoping Lu. A relaxation-type accelerating iteration method for large sparse horizontal nonlinear complementarity problems[J]. Electronic Research Archive, 2025, 33(12): 7442-7462. doi: 10.3934/era.2025328

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Abstract

In this work, a relaxation modulus-based matrix splitting iteration method for large sparse horizontal nonlinear complementarity problems was established. The convergence analysis was presented, where the proposed conditions were shown to be weaker than the existing result. Furthermore, a practical selection strategy of the relaxation parameter was provided by analyzing the error function in each iteration. Numerical examples were given to verify the theoretical improvement and show the effectiveness of the proposed method with the suggested relaxation parameters.

References

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