A power penalty method for a class of linearly constrained variational inequality

Abstract

This paper establishes new convergence results for the power pena-lty method for a mixed complementarity problem(MiCP). The power penalty method approximates the MiCP by a nonlinear equation containing a power penalty term. The main merit of the method is that it has an exponential convergence rate with the penalty parameter when the involved function is continuous and ξ-monotone. Under the same assumptions, we establish a new upper bound for the approximation error of the solution to the nonlinear equation. We also prove that the penalty method can handle general monotone MiCPs. Then the method is used to solve a class of linearly constrained variational inequality(VI). Since the MiCP associated with a linearly constrained VI does not ξ-monotone even if the VI is ξ-monotone, we establish the new convergence result for this MiCP. We use the method to solve the asymmetric traffic assignment problem which can be reformulated as a class of linearly constrained VI. Numerical results are provided to demonstrate the efficiency of the method.