On some NCP-functions based on the generalized Fischer–Burmeister function

In this paper, we study several NCP-functions for the nonlinear complementarity problem (NCP) which are indeed based on the generalized Fischer–Burmeister function, φp(a,b) = ‖(a,b)‖p − (a + b). It is well known that the NCP can be reformulated as an equivalent unconstrained minimization by means of merit functions involving NCP-functions. Thus, we aim to investigate some important properties of these NCP-functions that will be used in solving and analyzing the reformulation of the NCP.