First and second order conditions for optimal control problems with an L0 term in the cost functional
In this paper, we investigate optimal control problems subject to a semilinear elliptic partial differential equation. The cost functional contains a term that measures the size of the support of the control, which is the so-called L0-norm. We provide necessary and sufficient optimality conditions o...
| Autores: | , |
|---|---|
| Tipo de documento: | artigo |
| Data de publicação: | 2020 |
| País: | España |
| Recursos: | Universidad de Cantabria (UC) |
| Repositório: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Idioma: | inglês |
| OAI Identifier: | oai:repositorio.unican.es:10902/20289 |
| Acesso em linha: | http://hdl.handle.net/10902/20289 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Optimal control Semilinear partial differential equation Optimality conditions Sparse controls |
| Resumo: | In this paper, we investigate optimal control problems subject to a semilinear elliptic partial differential equation. The cost functional contains a term that measures the size of the support of the control, which is the so-called L0-norm. We provide necessary and sufficient optimality conditions of second order. The sufficient second-order condition is obtained by analyzing a partially convexified problem. Interestingly, the structure of the problem yields second-order conditions with different bilinear forms for the necessary and for the sufficient conditions. |
|---|