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...

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Detalles Bibliográficos
Autores: Casas Rentería, Eduardo|||0000-0002-8364-9416, Tröltzsch, Fredi
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
Descripción
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.