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...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2020 |
| Country: | España |
| Institution: | Universidad de Cantabria (UC) |
| Repository: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Language: | English |
| OAI Identifier: | oai:repositorio.unican.es:10902/19005 |
| Online Access: | http://hdl.handle.net/10902/19005 |
| Access Level: | Open access |
| Keyword: | Heat equation Optimal control Sparse control Mixed control-state constraints |
| Summary: | 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. |
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