Some properties of a class of merit functions for symmetric cone complementarity problems

In this paper, we extend a class of merit functions proposed by Kanzow et al. for linear/nonlinear complementarity problems to Symmetric Cone Complementarity Problems (SCCP). We show that these functions have several interesting properties, and establish a global error bound for the solution to the SCCP as well as the level boundedness of every merit function under some mild assumptions. Moreover, several functions are demonstrated to enjoy these properties.