Non-interior continuation method for complementarity problems in absence of strict complementarity

In this paper, by using a modified smoothing function, we propose a new continuation method for complementarity problems with R0-function and P0-function in the absence of strict complementarity. At each iteration, the continuation method solves one linear system of equations and performs one line search. When the underlying mapping is both a P0-function and an R0-function and its Hessian is Lipschitz continuous, we prove the global convergence of the new method. The new method also has global Q-linear and local Q-quadratical convergence rates under the same conditions.