Control of distributed parameter systems modelled by parabolic variational inequalities of the obstacle type

Abstract

We will investigate the numerical solution of the control problem modelled by parabolic variational inequalities. The general point of view adopted in this work has its roots in the work by R. Glowinski. The optimal control of parabolic variational inequalities is a hot topic in the control of distributed parameter system, since the classical optimality conditions such as KKT conditions do not apply and tools from non-smooth analysis have to be used. We demonstrate the simple approach to address optimal control of parabolic variational inequalities. First, we will introduce the model and describe the solution method. In Section 4 and 5, we will discuss the discretization of the model problem and then a conjugate gradient algorithm for solving the problem numerically. Finally we will present numerical results of optimal control problem related to variational inequality.