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Solution of nonsmooth generalized complementarity problems. (English) Zbl 1228.90131
Summary: We consider an unconstrained minimization reformulation of the generalized complementarity problem GCP(f,g) when the underlying functions f and g are H-differentiable. We describe H-differentials of some GCP functions based on the min function and the penalized Fischer-Burmeister function, and their merit functions. Under appropriate semimonotone, strictly semimonotone regularity-conditions on the H-differentials of f and g, we show that a local/global minimum of a merit function (or a “stationary point” of a merit function) is coincident with the solution of the given generalized complementarity problem. When specialized GCP(f,g) to the nonlinear complementarity problems, our results not only give new results but also extend/unify various similar results proved for C 1 , semismooth, and locally Lipschitzian.
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)