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

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.

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

 Autoría: Casas E., Mateos M., Rösch A.,

 Fuente: Computational Optimization and Applications, 2018, 70(1), 239-266

Editorial: Springer Nature

 Fecha de publicación: 01/05/2018

Nº de páginas: 26

Tipo de publicación: Artículo de Revista

DOI: 10.1007/s10589-018-9979-0

ISSN: 0926-6003,1573-2894

Proyecto español: MTM2014-57531-P ; MTM2017-83185-P

Url de la publicación: https://doi.org/10.1007/s10589-018-9979-0