Unconstrained methods for generalized complementarity problems

In this paper, the generalized complementarity problem is formulated as an unconstrained optimization problem. Our results generalize the results of [9]. The dimensionality of the unconstrained problem is the same as that of the original problem. If the mapping of generalized complementarity problem is differentiable, the objective function of the unconstrained problem is also differentiable. All the solutions of the original problem are global minimizers of the optimization problem. A generalized strict complementarity condition is given. Under certain assumptions, local properties of the correspondent unconstrained optimization problem are studied. Limited numerical tests are also reported.