Sparse optimal control for the heat equation with mixed control-state constraints

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URI: http://hdl.handle.net/10902/19005
ISSN: 2156-8472
ISSN: 2156-8499
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Autoría
Casas Rentería, EduardoAutoridad Unican; Tröltzsch, FrediAutoridad Unican
Fecha
2020-09
Derechos
© American Institute of Mathematical Sciences. This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Mathematical Control and Related Fields following peer review. The definitive publisher-authenticated version Casas, E., Tröltzsch, F. Sparse optimal control for the heat equation with mixed control-state constraints. Mathematical Control and Related Fields, 2020, 10 (3), 471-491. doi: 10.3934/mcrf.2020007 is available online at: https://www.aimsciences.org/article/doi/10.3934/mcrf.2020007
Publicado en
Mathematical Control and Related Fields, 2020, 10(3), 471-491
Editorial
American Institute of Mathematical Sciences
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Palabras clave
Heat equation
Optimal control
Sparse control
Mixed control-state constraints
Resumen/Abstract
A problem of sparse optimal control for the heat equation is considered, where pointwise bounds on the control and mixed pointwise control-state constraints are given. A standard quadratic tracking type functional is to be minimized that includes a Tikhonov regularization term and the L1-norm of the control accounting for the sparsity. Special emphasis is laid on existence and regularity of Lagrange multipliers for the mixed control-state constraints. To this aim, a duality theorem for linear programming problems in Hilbert spaces is proved and applied to the given optimal control problem.
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