Acta mathematica scientia,Series A ›› 2025, Vol. 45 ›› Issue (4): 1311-1326.

Previous Articles     Next Articles

The Levenberg-Marquardt Algorithm for Solving the Generalized Complementarity Problems

Yu Dongmei*(),Liu Dayi   

  1. College of Science, Liaoning Technical University, Liaoning Fuxin 123000
  • Received:2024-09-05 Revised:2025-04-13 Online:2025-08-26 Published:2025-08-01
  • Supported by:
    Supported by the Natural Science Foundation of Liaoning Province(2024-MS-206);Liaoning Provincial Department of Education(JYTZD2023072);Liaoning Provincial Department of Education(LJ112410147046);Liaoning Provincial Department of Education(LJ242410147027)

Abstract:

In this paper, the Levenberg-Marquardt type method is proposed for solving the generalized complementarity problems. Firstly, by integrating a class of complementary functions, the generalized complementarity problem is equivalently reformulated as a system of nonlinear equations. An adaptive modified Levenberg-Marquardt algorithm with line search is then introduced to address this reformulated problem. Furthermore, the convergence of the proposed algorithm is analyzed under appropriate conditions. Finally, numerical experiments are conducted to verify the feasibility and effectiveness of the proposed algorithm.

Key words: generalized complementarity problem, Levenberg-Marquardt algorithm, line search, convergence analysis

CLC Number: 

  • O224
Trendmd