On numerical solution of hemivariational inequalities by nonsmooth optimization methods

In this paper we consider numerical solution of hemivariational inequalities (HVI) by using nonsmooth, nonconvex optimization methods. First we introduce a finite element approximation of (HVI) and show that it can be transformed to a problem of finding a substationary point of the corresponding potential function. Then we introduce a proximal budle method for nonsmooth nonconvex and constrained optimization. Numerical results of a nonmonotone contact problem obtained by the developed methods are also presented.