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.