Two classes of merit functions for the second-order cone complementarity problem

Recently Tseng [Merit function for semidefinite complementarity, Mathematical Programming, 83, pp. 159-185, 1998] extended a class of merit functions, proposed by Z. Luo and P. Tseng [A new class of merit functions for the nonlinear complementarity problem, in Complementarity and Variational Problems: State of the Art, pp. 204-225, 1997], for the nonlinear complementarity problem (NCP) to the semidefinite complementarity problem (SDCP) and showed several related properties. In this paper, we extend this class of merit functions to the second-order cone complementarity problem (SOCCP) and show analogous properties as in NCP and SDCP cases. In addition, we study another class of merit functions which are based on a slight modification of the aforementioned class of merit functions. Both classes of merit functions provide an error bound for the SOCCP and have bounded level sets.