Abstract
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.
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