State-Constrained Optimization of PDEs via Infinite Penalization Methods

We consider optimization problems constrained by partial differential equations (PDEs) with additional constraints placed on the solution of the PDEs. Specifically, we consider problems involving constraints on the average value of the state in subdomains. We develop a general framework using infinite-valued penalization functions and Clarke generalized gradients to obtain optimality conditions. A numerical example involving a linear elliptic PDE is presented. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)