A globally convergent method based on Fischer–Burmeister operators for solving second-order cone constrained variational inequality problems

Abstract

The Karush–Kuhn–Tucker system of a second-order cone constrained variational inequality problem is transformed into a semismooth system of equations with the help of Fischer–Burmeister operators over second-order cones. The Clarke generalized differential of the semismooth mapping is presented. A modified Newton method with Armijo line search is proved to have global convergence with local superlinear rate of convergence under certain assumptions on the variational inequality problem. An illustrative example is given to show how the globally convergent method works.