Global Newton-type methods and semismooth reformulations for NCP

It is known that a nonlinear complementarity problem (NCP) can be reformulated as a semismooth system of nonlinear equations by using a so-called NCP-function. Global Newton-type methods for solving NCP via semismooth reformulation need to use a merit function, which is usually required to be continuously differentiable. In this paper we present a global Newton-type method which does not require the differentiability for the merit function used in the line-search procedure. The method is used to numerically compare the effectiveness of two NCP-functions widely discussed in literature, the minimum function and the Fischer–Burmeister function. The results on several examples allow to gain some new acquaintance of the respective numerical advantages of the two functions.