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Optimality Conditions for State-Constrained PDE Control Problems with Time-Dependent Controls

Please always quote using this URN:urn:nbn:de:0296-matheon-4701
  • The paper deals with optimal control problems for semilinear elliptic and parabolic PDEs subject to pointwise state constraints. The main issue is that the controls are taken from a restricted control space. In the parabolic case, they are vector-valued functions of the time, while they are vectors in elliptic problems. Under natural assumptions, first- and second-order sufficient optimality conditions are derived. The main result is the extension of second-order sufficient conditions to semilinear parabolic equations in domains of arbitrary dimension. In the elliptic case, the problems can be handled by known results of semi-infinite optimization. Here, different examples are discussed that exhibit different forms of active sets and where second-order sufficient conditions are satisfied at the optimal solution.

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Metadaten
Author:Juan Carlos de Los Reyes, Pedro Merino, Joachim Rehberg, Fredi Tröltzsch
URN:urn:nbn:de:0296-matheon-4701
Referee:Jürgen Sprekels
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2008/11/03
Release Date:2008/02/28
Preprint Number:472
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