First- and second-order optimality conditions for a class of optimal control problems with quasilinear elliptic equations
A class of optimal control problems for quasilinear elliptic equations is considered, where the coefficients of the elliptic differential operator depend on the state function. First- and second-order optimality conditions are discussed for an associated control-constrained optimal control problem....
| Autores: | , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2009 |
| País: | España |
| Recursos: | Universidad de Cantabria (UC) |
| Repositório: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Idioma: | inglês |
| OAI Identifier: | oai:repositorio.unican.es:10902/1636 |
| Acesso em linha: | http://hdl.handle.net/10902/1636 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Optimal control Distributed control Quasilinear elliptic equations Pontryagin maximum principle Second order optimality conditions |
| Resumo: | A class of optimal control problems for quasilinear elliptic equations is considered, where the coefficients of the elliptic differential operator depend on the state function. First- and second-order optimality conditions are discussed for an associated control-constrained optimal control problem. Main emphasis is laid on second-order sufficient optimality conditions. To this aim, the regularity of the solutions to the state equation and its linearization is studied in detail and the Pontryagin maximum principle is derived. One of the main difficulties is the nonmonotone character of the state equation. |
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