A Modulus-Based Shamanskii-Like Levenberg-Marquardt Method for Solving Nonlinear Complementary Problems

In this paper, a modulus-based Shamanskii-Like Levenberg-Marquardt method is proposed for solving nonlinear complementarity problems (NCPs). First, the NCP is reformulated in the form of an equivalent non-smooth system of equations. Then, a non-smooth Shamanskii-Like Levenberg-Marquardt method using a non-monotone r-order Armijo line search is developed by generalizing a smooth Levenberg-Marquardt method to solve the resulting system. Global convergence of the proposed method is achieved under some suitable assumptions. Numerical experiments verify the feasibility and efficiency of the proposed method.