@article{10902/19005,
year = {2020},
month = {9},
url = {http://hdl.handle.net/10902/19005},
abstract = {A problem of sparse optimal control for the heat equation is considered, where pointwise bounds on the control and mixed pointwise control-state constraints are given. A standard quadratic tracking type functional is to be minimized that includes a Tikhonov regularization term and the L1-norm of the control accounting for the sparsity. Special emphasis is laid on existence and regularity of Lagrange multipliers for the mixed control-state constraints. To this aim, a duality theorem for linear programming problems in Hilbert spaces is proved and applied to the given optimal control problem.},
organization = {The first author was partially supported by Spanish Ministerio de Economía, Industria y Competitividad under projects MTM2014-57531-P and MTM2017-83185-P. The second author was supported by the Collaborative Research Center SFB 910, TU Berlin, project B6.},
publisher = {American Institute of Mathematical Sciences},
publisher = {Mathematical Control and Related Fields, 2020, 10(3), 471-491},
title = {Sparse optimal control for the heat equation with mixed control-state constraints},
author = {Casas Rentería, Eduardo and Tröltzsch, Fredi},
}