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.
Author: | Juan Carlos de Los Reyes, Pedro Merino, Joachim Rehberg, Fredi Tröltzsch |
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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 |