An inexact semismooth Newton method for variational inequality with symmetric cone constraints

Abstract

In this paper, weconsider using the inexact nonsmooth Newton method to efficientlysolve the symmetric cone constrained variational inequality (VISCC)problem. It red provides a unified framework for dealingwith the variational inequality with nonlinear constraints,variational inequality with the second-order cone constraints, andthe variational inequality with semidefinite cone constraints. Weget convergence of the above method and apply the results to three special types symmetric cones.