A smoothing Levenberg-Marquardt algorithm for linear weighted complementarity problem

Panjie Tian; Zhensheng Yu; Yue Yuan; Panjie Tian; Zhensheng Yu; Yue Yuan

doi:10.3934/math.2023498

AIMS Mathematics

2023, Volume 8, Issue 4: 9862-9876. doi: 10.3934/math.2023498

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Research article

A smoothing Levenberg-Marquardt algorithm for linear weighted complementarity problem

College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Received: 21 December 2022 Revised: 28 January 2023 Accepted: 31 January 2023 Published: 22 February 2023
MSC : 65K05, 90C33

In this paper, we consider the solution of linear weighted complementarity problem (denoted by LWCP). Firstly, we introduce a new class of weighted complementary functions and show that its continuously differentiable. On this basis, the LWCP is reconstructed as a smooth system of equations, and then solved by the Levenberg-Marquardt method. The convergence of the algorithm is proved theoretically and numerical experiments are carried out. The comparative experiments show that the algorithm has some advantages in computing time and iteration times.
- linear weighted complementarity problem,
- smooth function,
- L-M method
Citation: Panjie Tian, Zhensheng Yu, Yue Yuan. A smoothing Levenberg-Marquardt algorithm for linear weighted complementarity problem[J]. AIMS Mathematics, 2023, 8(4): 9862-9876. doi: 10.3934/math.2023498

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Abstract

In this paper, we consider the solution of linear weighted complementarity problem (denoted by LWCP). Firstly, we introduce a new class of weighted complementary functions and show that its continuously differentiable. On this basis, the LWCP is reconstructed as a smooth system of equations, and then solved by the Levenberg-Marquardt method. The convergence of the algorithm is proved theoretically and numerical experiments are carried out. The comparative experiments show that the algorithm has some advantages in computing time and iteration times.

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