Analysis of optimal control problems of semilinear elliptic equations by BV-functions

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URI: http://hdl.handle.net/10902/16321
ISSN: 1877-0533
ISSN: 1877-0541
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Autoría
Casas Rentería, EduardoAutoridad Unican; Kunisch, Karl
Fecha
2019-06
Derechos
© Springer. This is a post-peer-review, pre-copyedit version of an article published Set-Valued and Variational Analysis. The final authenticated version is available online at: https://doi.org/10.1007/s11228-018-0482-7
Publicado en
Set-Valued and Variational Analysis, 2019, 27(2), 355-379
Editorial
Springer
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Palabras clave
Optimal control
Bounded variation functions
Sparsity
First and second order optimality conditions
Semilinear elliptic equations
Resumen/Abstract
Optimal control problems for semilinear elliptic equations with control costs in the space of bounded variations are analysed. BV-based optimal controls favor piecewise constant, and hence ’simple’ controls, with few jumps. Existence of optimal controls, necessary and sufficient optimality conditions of first and second order are analysed. Special attention is paid on the effect of the choice of the vector norm in the definition of the BV-seminorm for the optimal primal and adjoined variables.
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