A modulus-based modified multivariate spectral gradient projection method for solving the horizontal linear complementarity problem

Ting Lin; Hong Zhang; Chaofan Xie; Ting Lin; Hong Zhang; Chaofan Xie

doi:10.3934/math.2025151

AIMS Mathematics

2025, Volume 10, Issue 2: 3251-3268. doi: 10.3934/math.2025151

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A modulus-based modified multivariate spectral gradient projection method for solving the horizontal linear complementarity problem

1.
School of Big Data and Artificial Intelligence, Fujian Polytechnic Normal University, Fuqing 350300, China
2.
Key Laboratory of Nondestructive Testing, Fujian Province University, Fuqing 350300, China

Received: 30 September 2024 Revised: 14 December 2024 Accepted: 02 January 2025 Published: 20 February 2025
MSC : 65F45, 65G99, 65H20, 90C30

In this research, we investigated the nonnegative cone horizontal linear complementarity problem (HLCP). Initially, we transformed the HLCP into a fixed-point equation using the modulus defined within the nonnegative cone. By redefining this fixed-point equation as a monotone system, we introduced an improved multivariate spectral gradient projection method for solving it. This study shows that the proposed iterative method converges to the solution of the HLCP, assuming the specified conditions are met. Additionally, numerical examples were included to illustrate the practicality and effectiveness of the modulus-based enhanced multivariate spectral gradient projection method in computational settings.
- horizontal linear complementarity problem,
- modulus-based algorithm,
- multivariate spectral gradient projection,
- nonnegative cone,
- monotone system
Citation: Ting Lin, Hong Zhang, Chaofan Xie. A modulus-based modified multivariate spectral gradient projection method for solving the horizontal linear complementarity problem[J]. AIMS Mathematics, 2025, 10(2): 3251-3268. doi: 10.3934/math.2025151

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Abstract

In this research, we investigated the nonnegative cone horizontal linear complementarity problem (HLCP). Initially, we transformed the HLCP into a fixed-point equation using the modulus defined within the nonnegative cone. By redefining this fixed-point equation as a monotone system, we introduced an improved multivariate spectral gradient projection method for solving it. This study shows that the proposed iterative method converges to the solution of the HLCP, assuming the specified conditions are met. Additionally, numerical examples were included to illustrate the practicality and effectiveness of the modulus-based enhanced multivariate spectral gradient projection method in computational settings.

References

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