A level set approach for the solution of a state-constrained optimal control problem |
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Authors: | Michael Hintermüller Wolfgang Ring |
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Institution: | (1) Deptartment of Computational and Applied Mathematics, Rice University, 6100 Main Street, Houston, TX 77005, USA;(2) Special Research Center on Optimization and Control, University of Graz, Institute of Mathematics, Heinrichstrasse 36, 8010 Graz, Austria |
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Abstract: | Summary. 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.Mathematics Subject Classification (1991): 35R35, 49K20, 49Q10, 65K10Revised version received March 19, 2003 |
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