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State error estimates for the numerical approximation of sparse distributed control problems in the absence of Tikhonov regularization

Abstract: In this paper, we analyze optimal control problems of semilinear elliptic equations, where the controls are distributed. Box constraints for the controls are imposed and the cost functional does not involve the control itself, except possibly for a non-differentiable sparsity-promoting term. Under appropriate second order sufficient optimality conditions, first we estimate the difference between the dis crete and continuous optimal states. Next, under an additional assumption on the optimal adjoint state, we prove error estimates for the controls and improve the estimates for the states.

 Autoría: Casas E., Mateos M.,

 Fuente: Vietnam Journal of Mathematics, 2021, 49(3), 713-738 - (CORRIGENDUM), 2023, 51(2), 565-566

 Editorial: Springer Science + Business Media

 Fecha de publicación: 01/09/2021

 Nº de páginas: 28

 Tipo de publicación: Artículo de Revista

 DOI: 10.1007/s10013-021-00491-x

 ISSN: 2305-221X,2305-2228

 Proyecto español: MTM2017-83185-P

 Url de la publicación: https://doi.org/10.1007/s10013-021-00491-x