Sufficient second-order optimality conditions for semilinear control problems with pointwise state constraints

Second-order sufficient optimality conditions are established for the optimal control of semilinear elliptic and parabolic equations with pointwise constraints on the control and the state. In contrast to former publications on this subject, the cone of critical directions is the smallest possible i...

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Detalles Bibliográficos
Autores: Casas Rentería, Eduardo|||0000-0002-8364-9416, Reyes, Juan Carlos de los, Tröltzsch, Fredi
Tipo de recurso: artículo
Fecha de publicación:2008
País:España
Institución:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/2211
Acceso en línea:http://hdl.handle.net/10902/2211
Access Level:acceso abierto
Palabra clave:Optimal control
Elliptic equations
Parabolic equations
Pointwise state constraints
Second-order necessary optimality conditions
Second-order sufficient optimality conditions
Descripción
Sumario:Second-order sufficient optimality conditions are established for the optimal control of semilinear elliptic and parabolic equations with pointwise constraints on the control and the state. In contrast to former publications on this subject, the cone of critical directions is the smallest possible in the sense that the second-order sufficient conditions are the closest to the associated necessary ones. The theory is developed for elliptic distributed controls in domains up to dimension three. Moreover, problems of elliptic boundary control and parabolic distributed control are discussed in spatial domains of dimension two and one, respectively.