Abstract: A class of merit functions for describing the nonlinear complementarity problems (NCP) was extended to that for describing the symmetric cone complementarity (SCCP) problems by the tool of Euclidean-Jordan algebras. And then it was shown that the SCCP is equivalent to an unconstrained smooth minimizationvia this new merit function and two examples of the class of merit function are given. Moreover, the conditions under which the new merit function provides a global error bound were studied with a weak condition given under which the new merit function has bounded level sets.

Key words: complementarity problems, symmetric cone, merit function, EuclideanJordan algebra