Second-order optimality conditions for weak and strong local solutions of parabolic optimal control problems

Second-order sufficient optimality conditions are considered for a simplified class of semilinear parabolic equations with quadratic objective functional including distributed and terminal observation. Main emphasis is laid on problems where the objective functional does not include a Tikhonov regul...

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Detalles Bibliográficos
Autores: Casas Rentería, Eduardo|||0000-0002-8364-9416, Tröltzsch, Fredi
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/11155
Acceso en línea:http://hdl.handle.net/10902/11155
Access Level:acceso abierto
Palabra clave:Optimal control
Parabolic equations
Semilinear equation
Second order optimality conditions
Weak local minimum
Strong local minimum
Descripción
Sumario:Second-order sufficient optimality conditions are considered for a simplified class of semilinear parabolic equations with quadratic objective functional including distributed and terminal observation. Main emphasis is laid on problems where the objective functional does not include a Tikhonov regularization term. Here, standard second-order conditions cannot be expected to hold. For this case, new second-order conditions are established that are based on different types of critical cones. Depending on the choice of this cones, the second-order conditions are sufficient for local minima that are weak or strong in the sense of calculus of variations.