Lagrangian methods for optimal control problems governed by a mixed quasi-variational inequality

Abstract

This paper studies an optimal control problem where the state of the system is defined by a mixed quasi-variational inequality. Several sufficient conditions for the zero duality gap property between the optimal control problem and its nonlinear dual problem are obtained by using nonlinear Lagrangian methods. Our results are applied to an example where the mixed quasi-variational inequality leads to a bilateral obstacle problem.