In this paper sufficient second order optimality conditions for optimal control problemssubject to stationary variational inequalities of obstacle type are derived. Sinceoptimality conditions for such problems always involve measures as Lagrange multipliers,which impede the use of efficient Newton type methods, a family of regularized problems isintroduced. Second order sufficient optimality conditions are derived for the regularizedproblems as well. It is further shown that these conditions are also sufficient forsuperlinear convergence of the semi-smooth Newton algorithm to be well-defined andsuperlinearly convergent when applied to the first order optimality system associated withthe regularized problems.
