Optimization of mixed variational inequalities arising in flow of viscoplastic materials

Optimal control problems of mixed variational inequalities of the second kind arising in flow of Bingham viscoplastic materials are considered. Two type of active-inactive set regularizing functions for the control problems are proposed and approximation properties and optimality conditions are investigated. A detailed first order optimality system for the control problem is obtained as limit of the regularized optimality conditions. For the solution of each regularized system a globalized semismooth Newton algorithm is constructed and its computational performance is investigated.