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

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...

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Detalhes bibliográficos
Autores: Casas Rentería, Eduardo|||0000-0002-8364-9416, Tröltzsch, Fredi
Formato: artículo
Fecha de publicación:2020
País:España
Recursos:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/19005
Acesso em linha:http://hdl.handle.net/10902/19005
Access Level:acceso abierto
Palavra-chave:Heat equation
Optimal control
Sparse control
Mixed control-state constraints
Descrição
Resumo: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.