Department of Applied Mathematics & Physics, Kyoto Univiversity

Technical Report #97006 (June, 1997)

A new merit function and a descent method for semidefinite complementarity problems
by Nobuo Yamashita and Masao Fukushima

Recently, Tseng extended several merit functions for the nonlinear complementarity problem to the semidefinite complementarity problem (SDCP) and investigated various properties of those functions. In this paper, we propose a new merit function for the SDCP based on the squared Fischer-Burmeister function and show that it has some favorable properties. Particularly, we give conditions under which the function provides a global error bound for the SDCP and conditions under which it has bounded level sets. We also present a derivative-free method for solving the SDCP and prove its global convergence under suitable assumptions.