Second order analysis for optimal control problems: improving results expected from abstract theory
An abstract optimization problem of minimizing a functional on a convex subset of a Banach space is considered. We discuss natural assumptions on the functional that permit establishing sufficient second-order optimality conditions with minimal gap with respect to the associated necessary ones. Though...
| Autores: | , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2012 |
| País: | España |
| Recursos: | Universidad de Cantabria (UC) |
| Repositório: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Idioma: | inglês |
| OAI Identifier: | oai:repositorio.unican.es:10902/2200 |
| Acesso em linha: | http://hdl.handle.net/10902/2200 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Optimal control Semilinear partial differential equation Second order optimality conditions Quadratic growth condition Two-norm discrepancy |
| Resumo: | An abstract optimization problem of minimizing a functional on a convex subset of a Banach space is considered. We discuss natural assumptions on the functional that permit establishing sufficient second-order optimality conditions with minimal gap with respect to the associated necessary ones. Though the two-norm discrepancy is taken into account, the obtained results exhibit the same formulation as the classical ones known from finite-dimensional optimization. We demonstrate that these assumptions are fulfilled, in particular, by important optimal control problems for partial differential equations. We prove that, in contrast to a widespread common belief, the standard second-order conditions formulated for these control problems imply strict local optimality of the controls not only in the sense of L ∞, but also of L2 . |
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