A Two-Parametric Class of Merit Functions for the Second-Order Cone Complementarity Problem

We propose a two-parametric class of merit functions for the second-order cone complementarity problem (SOCCP) based on the one-parametric class of complementarity functions. By the new class of merit functions, the SOCCP can be reformulated as an unconstrainedminimization problem.The new class ofmerit functions is shown to possess some favorable properties. In particular, it provides a global error bound if F andG have the joint uniformCartesianP-property. And it has bounded level sets under aweaker condition than the most available conditions. Some preliminary numerical results for solving the SOCCPs show the effectiveness of the merit function method via the new class of merit functions.