Department of Applied Mathematics & Physics, Kyoto Univiversity

Technical Report #98015 (September, 1998)

The Extended Semidefinite Linear Complementarity Problem: A Reformulation Approach
by Masahiro Shibata, Nobuo Yamashita and Masao Fukushima

In this paper, we have proposed a class of merit
functions for the extended semidefinite linear
complementarity problem (XSDLCP).
The proposed merit functions consist of a smooth
exterior penalty function and either the squared
Fischer-Burmeister function or the implicit
Lagrangian. By using those merit functions,
we reformulated XSDLCP as unconstrained
minimization problems.
Furthermore we established sufficient conditions
which guarantee that any stationary point of
the merit functions is a solution of XSDLCP.
By using another merit function, we also gave
conditions for the existence of a solution of
SDNCP.