Computational Optimization and Applications

, Volume 43, Issue 2, pp 213–233

A virtual control concept for state constrained optimal control problems


DOI: 10.1007/s10589-007-9130-0

Cite this article as:
Krumbiegel, K. & Rösch, A. Comput Optim Appl (2009) 43: 213. doi:10.1007/s10589-007-9130-0


A linear elliptic control problem with pointwise state constraints is considered. These constraints are given in the domain. In contrast to this, the control acts only at the boundary. We propose a general concept using virtual control in this paper. The virtual control is introduced in objective, state equation, and constraints. Moreover, additional control constraints for the virtual control are investigated. An error estimate for the regularization error is derived as main result of the paper. The theory is illustrated by numerical tests.


Optimal controlElliptic equationState constraintsBoundary controlRegularizationVirtual control

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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Johann Radon Institute for Computational and Applied Mathematics (RICAM)Austrian Academy of SciencesLinzAustria