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Nonsmooth generalized complementarity as unconstrained optimization. (English) Zbl 1204.65071
The author considers the generalized complementarity problem with the underlying functionsbeing $H$-differentiable. He derives 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. He derives conditions on the underlying functions of the generalized complementarity problem to get a solution by introducing the concepts of relative monotonicity and ${P}_{0}$-property and their variants.
##### MSC:
 65K05 Mathematical programming (numerical methods) 90C33 Complementarity and equilibrium problems; variational inequalities (finite dimensions)