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.