Improved approximation rates for a parabolic control problem with an objective promoting directional sparsity

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URI: http://hdl.handle.net/10902/14819
ISSN: 0926-6003
ISSN: 1573-2894
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Autoría
Casas Rentería, EduardoAutoridad Unican; Mateos Alberdi, MarianoAutoridad Unican; Rösch, Arnd
Fecha
2018-05
Derechos
© Springer. This is a post-peer-review, pre-copyedit version of an article published in Computational Optimization and Applications. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10589-018-9979-0
Publicado en
Computational Optimization and Applications, 2018, 70(1), 239-266
Editorial
Springer Nature
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Palabras clave
Optimal control
Parabolic equations
Directionally sparse solutions
Finite element approximation
Numerical quadrature
Error estimates
Resumen/Abstract
We discretize a directionally sparse parabolic control problem governed by a linear equation by means of control approximations that are piecewise constant in time and continuous piecewise linear in space. By discretizing the objective functional with the help of appropriate numerical quadrature formulas, we are able to show that the discrete optimal solution exhibits a directional sparse pattern alike the one enjoyed by the continuous solution. Error estimates are obtained and a comparison with the cases of having piecewise approximations of the control or a semilinear state equation are discussed. Numerical experiments that illustrate the theoretical results are included.
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