EQUIVALENCE OF THE GENERALIZED COMPLEMENTARITY-PROBLEM TO DIFFERENTIABLE UNCONSTRAINED MINIMIZATION

We consider an unconstrained minimization reformulation of the general ized complementarity problem (GCP). The merit function introduced here is differentiable and has the property that its global minimizers coi ncide with the solutions of GCP. Conditions for its stationary points to be global minimizers are given. Moreover, it is shown that the leve l sets of the merit function are bounded under suitable assumptions. W e also show that the merit function provides global error bounds for G CP. These results are based on a condition which reduces to the condit ion of the uniform P-function when GCP is specialized to the nonlinear complementarity problem. This condition also turns out to be useful i n proving the existence and uniqueness of a solution for GCP itself. F inally, we obtain as a byproduct an error bound result with the natura l residual for GCP.