Multilevel optimization for PDAE‐constrained optimal control problems with pointwise constraints on control and state

Abstract

AbstractWe have developed a fully adaptive optimization environment suitable to solve complex optimal control problems restricted by partial differential algebraic equations (PDAEs) and pointwise constraints on the control [1, 2]. This contribution is devoted to the inclusion of pointwise constraints on the state within the optimization environment. To this end we first give a brief introduction into the architecture of the environment and the inclusion of pointwise constraints on the state by Moreau‐Yosida regularization. Then, we test the new tool by applying it to an optimal boundary control problem for the cooling of hot glass down to room temperature, modeled by radiative heat transfer and semi‐transparent boundary conditions. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)