A new smoothing quasi-Newton method for nonlinear complementarity problems

A new smoothing quasi-Newton method for nonlinear complementarity problems is presented. The method is a generalization of Thomas’ method for smooth nonlinear systems and has similar properties as Broydenʹs method. Local convergence is analyzed for a strictly complementary solution as well as for a degenerate solution. Presented numerical results demonstrate quite similar behavior of Thomas’ and Broydenʹs methods.