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Stability for semilinear parabolic optimal control problems with respect to initial data

Abstract: A distributed optimal control problem for a semilinear parabolic partial differential equation is investigated. The stability of locally optimal solutions with respect to perturbations of the initial data is studied. Based on different types of sufficient optimality conditions for a local solution of the unperturbed problem, Lipschitz or Hölder stability with respect to perturbations are proved. Moreover, a particular example with semilinear equation, constant initial data, and standard quadratic tracking type objective functional is constructed that has at least two different locally optimal solutions. By the perturbation analysis, the existence of a problem with non-constant initial data is shown that also has at least two different locally optimal solutions.

 Autoría: Casas E., Tröltzsch F.,

 Fuente: Applied Mathematics and Optimization, 2022, 86(2), 16

 Editorial: Springer

 Fecha de publicación: 06/07/2022

 Nº de páginas: 31

 Tipo de publicación: Artículo de Revista

 DOI: 10.1007/s00245-022-09888-7

 ISSN: 0095-4616,1432-0606

 Proyecto español: PID2020-114837GB-I00

 Url de la publicación: https://doi.org/10.1007/s00245-022-09888-7