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

Casas, Eduardo; Mateos, Mariano; Rösch, Arnd

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.

LINEAR equations; OPTIMAL control theory; DEGENERATE parabolic equations; PIECEWISE linear approximation; FINITE element method

Computational Optimization & Applications, 2018, Vol 70, Issue 1, p239

0926-6003

Academic Journal

10.1007/s10589-018-9979-0