A globally convergent Levenberg–Marquardt method for solving nonlinear complementarity problem

The nonlinear complementarity problem (denoted by NCP(F)) can be reformulated as the least l2-norm solution of a optimization problem. By introducing a new smoothing function, the problem is approximated by a family of parameterized optimization problems with twice continuously differentiable objective functions. Then a smoothing Levenberg–Marquardt method is applied to solve the parameterized optimization problems. The global convergence of the proposed method is proved under an assumption that the level set of the problem is compact.