A level set approach for the solution of a state-constrained optimal control problem

Authors:
Michael Hintermüller;Wolfgang Ring
Affiliations:
Rice University, Deptartment of Computational and Applied Mathematics, 6100 Main Street, TX 77005, Houston, USA;University of Graz, Institute of Mathematics, Special Research Center on Optimization and Control, Heinrichstrasse 36, 8010, Graz, Austria
Venue:
Numerische Mathematik
Year:
2004

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Abstract

State constrained optimal control problems for linear elliptic partial differential equations are considered. The corresponding first order optimality conditions in primal-dual form are analyzed and linked to a free boundary problem resulting in a novel algorithmic approach with the boundary (interface) between the active and inactive sets as optimization variable. The new algorithm is based on the level set methodology. The speed function involved in the level set equation for propagating the interface is computed by utilizing techniques from shape optimization. Encouraging numerical results attained by the new algorithm are reported on.