Asian Journal of Mathematics and Computer Research

The weighted linear complementarity problem (WLCP) is important for modeling a variety of economic equilibrium problems. However, most existing numerical methods for WLCP either require the problem to be monotone or rely on nonsingularity conditions to ensure fast convergence. To overcome these limitations, this paper proposes a two-step Levenberg-Marquardt type method (TS-LMM) for solving WLCPs. By incorporating a smooth weighted complementarity function, the WLCP is reformulated as a system of smooth nonlinear equations, which is then solved using the proposed algorithm. The method is proved to be globally convergent without the need for monotonicity. Furthermore, under a local error bound condition, the proposed method achieves a cubic convergence rate, which is faster than the quadratic convergence of existing Levenberg-Marquardt methods. Numerical results demonstrate that the proposed method outperforms existing Levenberg-Marquardt methods in both iteration count and CPU time.