Second-order and stability analysis for state-constrained elliptic optimal control problems with sparse controls
An optimal control problem for a semilinear elliptic partial differential equation is discussed subject to pointwise control constraints on the control and the state. The main novelty of the paper is the presence of the L1-norm of the control as part of the objective functional that eventually leads...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universidad de Cantabria (UC) |
| Repositorio: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unican.es:10902/4884 |
| Acceso en línea: | http://hdl.handle.net/10902/4884 |
| Access Level: | acceso abierto |
| Palabra clave: | Optimal control Semilinear elliptic partial differential equation Pointwise state constraints Sparse control First- and second-order optimality conditions Stability analysis |
| Sumario: | An optimal control problem for a semilinear elliptic partial differential equation is discussed subject to pointwise control constraints on the control and the state. The main novelty of the paper is the presence of the L1-norm of the control as part of the objective functional that eventually leads to sparsity of the optimal control functions. Second-order sufficient optimality conditions are analyzed. They are applied to show the convergence of optimal solutions for vanishing L2-regularization parameter for the control. The associated convergence rate is estimated. |
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