The well studied regularization methods for ill-posed systems of nonlinear equations, such as Tikhonov's Method, require differentiability at the solution. In this talk we will present recent developments in regularization methods for the nonlinear complementarity problem (NCP).

A typical strategy for solving an NCP is to reformulate it as a system of nonlinear equations and solve the problem with a Newton type method, that uses a generalized Jacobian. Since the reformulated NCP is not differentiable at the solution, it can not be regularized with standard methods for nonlinear systems of equations. This has lead to the development of several efficient Regularized Newton methods, which handle the difficulty of a nearly singular generalized Jacobian, and also have fast convergence rates when the function is well defined at the solution. We will discuss these methods and their convergence results.