Optimal distributed control of the wave equation subject to state constraints

Abstract

The Lavrentiev regularization method is a tool to improve the regularity of the Lagrange multipliers in pde constrained optimal control problems with state constraints. It has already been used for problems with parabolic and elliptic systems. In this paper we consider Lavrentiev regularization for problems with a hyperbolic system, namely the scalar wave equation. We show that also in this case the regularization yields multipliers in the Hilbert space L2. We present numerical exam-ples, where we compare the Lavrentiev regularization, Lavrentiev Prox regularization, a fixed point iteration to improve feasibility, and a penalty method. © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.