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Nonsmooth generalized complementarity as
unconstrained optimization
We consider generalized complementarity problem GCP$(f,g)$ when the
underlying functions $f$ and $g$ are $H$-differentiable. We
describe $H$-differentials of some GCP functions and their
merit functions. We give some conditions on the $H$-differentials
of the given functions under which minimizing a merit function
corresponding to such functions leads to a solution of the
generalized complementarity problem. Further, we give some
conditions on the functions $f$ and $g$ to get a solution of
GCP$(f,g)$ by introducing the concepts of relative monotonicity and
P0-property and their variants. Our results further give a
unified/generalization treatment of such results for the nonlinear
complementarity problem when the underlying function is $C^1$ ,
semismooth, and locally Lipschitzian.