Analysis of spatio-temporally sparse optimal control problems of semilinear parabolic equations

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URI: http://hdl.handle.net/10902/10481
ISSN: 1292-8119
ISSN: 1262-3377
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Autoría
Casas Rentería, EduardoAutoridad Unican; Herzog, Roland; Wachsmuth, Gerd
Fecha
2017-01
Derechos
© EDP Sciences, SMAI, 2017. The original publication is available at www.esaim-cocv.org
Publicado en
ESAIM: Control, Optimisation and Calculus of Variations, 2017, 23 (1), 263-295
Editorial
EDP Sciences
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Palabras clave
Optimal control
Directional sparsity
Second-order optimality conditions
Semilinear parabolic equations
Resumen/Abstract
Optimal control problems with semilinear parabolic state equations are considered. The objective features one out of three different terms promoting various spatio-Temporal sparsity patterns of the control variable. For each problem, first-order necessary optimality conditions, as well as secondorder necessary and sufficient optimality conditions are proved. The analysis includes the case in which the objective does not contain the squared norm of the control.
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