Sparse optimal control for the heat equation with mixed control-state constraints

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.

 Autoría: Casas E., Tröltzsch F.,

 Fuente: Mathematical Control and Related Fields, 2020, 10(3): 471-491

Editorial: American Institute of Mathematical Sciences

 Fecha de publicación: 01/09/2020

Nº de páginas: 21

Tipo de publicación: Artículo de Revista

DOI: 10.3934/mcrf.2020007

ISSN: 2156-8472,2156-8499

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

Url de la publicación: https://doi.org/10.3934/mcrf.2020007