Recently,Tseng extended a class of merit functions for the nonlinear complementarity problem to semidefinite complementarity problem (SDCP), showing some properties under suitable assumptions. Yamashita and Fukushima also presented other properties. In this paper, we propose a new class of merit functions for the SDCP, and prove some of those properties, under weaker hypothesis. Particularly, we obtained conditions under which those merit functions provide a global error bound for SDCP, and conditions that guarantee bounded level sets.
ES-569, Programa de Engenharia de sistemas e Computação/COPPE/Federal University of Rio de Janeiro, January/2002