Symmetrization of generalized natural residual function for NCP

In contrast to the generalized Fischer–Burmeister function that is a natural extension of the popular Fischer–Burmeister function NCP-function, the generalized natural residual NCP-function based on discrete extension, recently proposed by Chen, Ko, and Wu, does not possess symmetric graph. In this paper we symmetrize the generalized natural residual NCP-function, and construct not only new NCP-functions and merit functions for the nonlinear complementarity problem, but also provide parallel functions to the generalized Fischer–Burmeister function.