On numerical solution of hemivariational inequalities by nonsmooth optimization methods (Q1905959)

In the paper the authors consider numerical solution of hemivariational inequalities (HVI) by using nonsmooth, nonconvex optimization methods. First, they 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 they introduce a proximal bundle method for nonsmooth nonconvex and constrained optimization. Numerical results of a nonmonotone contact problem obtained by the developed methods are also presented.