Interior point techniques for optimal control of variational inequalities

This paper is devoted to a new application of an interior point algorithm to solve optimal control problems of variational inequalities. We propose a Lagrangian technique to obtain a necessary optimality system. After the discretization of the optimality system we prove its equivalence to Karush-Kuhn-Tucker conditions of a nonlinear regular minimization problem. This problem can be efficiently solved by using a modification of Herskovits' interior point algorithm for nonlinear optimization. We describe the numerical scheme for solving this problem and give some numerical examples of test problems in 1-D and 2-D.