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Coerciveness of some merit functions over symmetric cones
Complementarity problems over symmetric cones (SCCP) can be
reformulated as the global minimization of a certain merit function.
The coerciveness of the merit function plays an important role in
this class of methods. In this paper, we introduce a class of merit
functions which contains the Fischer-Burmeister merit function and
the natural residual merit function as special cases, and prove the
coerciveness of this class of merit functions under some conditions
which are strictly weaker than the assumption that the function
involving in the SCCP is strongly monotone and Lipschitz continuous.
Based on the introduced merit function, we propose another class of
merit functions which is an extension of Fukushima-Yamashita merit
function. We investigate the coerciveness of the generalized
Fukushima-Yamashita merit function under a condition which is
strictly weaker than the assumption that the function involving in
the SCCP is weakly coercive. The theory of Euclidean Jordan algebras
is a basic tool in our analysis.