@article{10902/14819,
year = {2018},
month = {5},
url = {http://hdl.handle.net/10902/14819},
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.},
organization = {The first two authors were partially supported by the Spanish Ministerio de Economía y Competitividad under projects MTM2014-57531-P and MTM2017-83185-P.},
publisher = {Springer Nature},
publisher = {Computational Optimization and Applications, 2018, 70(1), 239-266},
title = {Improved approximation rates for a parabolic control problem with an objective promoting directional sparsity},
author = {Casas Rentería, Eduardo and Mateos Alberdi, Mariano and Rösch, Arnd},
}