Superlinearly convergent methods for solving a class of implicit complementarity problems based on sign analysis

In this paper, for the implicit complementarity problem, it is shown that the solution's sign patterns can be calculated via solving a linear system under some assumptions. Next, Newton iteration is applied to a equivalent nonlinear equation with quadratic convergence and the non-singularity of the Jacobian is discussed. Moreover, a superlinearly convergent hybrid method is established by combining an existing globally convergent iteration and the Newton iteration. Numerical examples show that the proposed methods have higher precision and converge faster than some existing methods.