In this paper we present an abstract nonsmooth optimization problem for which we recall existence and uniqueness results. We show a numerical scheme to approximate its solution. The theory is later applied to a sample static contact problem describing an elastic body in frictional contact with a foundation. This problem leads to a hemivariational inequality which we solve numerically. Finally, we compare three computational methods of solving contact mechanical problems: direct optimization method, augmented Lagrangian method and primal-dual active set strategy.

翻译：本文提出一个抽象非光滑优化问题，回顾其解的存在性与唯一性结果，并给出逼近解的数值格式。随后将该理论应用于描述弹性体与基础摩擦接触的静态接触问题实例，该问题导出半变分不等式并得以数值求解。最后，我们比较了三种求解接触力学问题的计算方法：直接优化法、增广拉格朗日法以及原始-对偶有效集策略。