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.


To appear on Applied Numerical Mathematics