NON-INTERIOR CONTINUATION METHOD FOR COMPLEMENTARITY PROBLEMS IN ABSENCE OF STRICT COMPLEMENTARITY
Min Sun () and
Zhen-Jun Shi ()
Additional contact information Min Sun: Department of Mathematics and Information Science, Zaozhuang University, Zaozhuang, Shandong, 277160, P. R. China
Zhen-Jun Shi: College of Operations Research and Management, Qufu Normal University, Rizhao, Shandong 276826, P. R. China; Department of Computer and Information Science, University of Michigan, Dearborn MI 48128, USA
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 a 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.