Abstract
We consider an unconstrained minimization reformulation of the complementarity problem (CP) on Rn. The merit function introduced here is by using Fukushima’s regularized gap function and it is proved that the global minimizers coincide with the solution of CP. This paper also shows that even if (Ψ1, Ψ2) — monotone generalizes the classical definition of monotone, there is no guarantee on the existence and uniqueness of the solution of the complementarity problem associated with hemicontinuous (Ψ1, Ψ2) — monotone mapping of convex cones.
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