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On optimal control problems with controls appearing nonlinearly in an elliptic state equation

Abstract: An optimal control problem for a semilinear elliptic equation is discussed, where the control appears nonlinearly in the state equation but is not included in the objective functional. The existence of optimal controls is proved by a measurable selection technique. First-order necessary optimality conditions are derived and two types of second-order sufficient optimality conditions are established. A first theorem invokes a well-known assumption on the set of zeros of the switching function. A second relies on coercivity of the second derivative of the reduced objective functional. The results are applied to the convergence of optimal state functions for a finite element discretizion of the control problem.

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

 Autoría: Casas E., Tröltzsch F.,

 Fuente: SIAM Journal on Control and Optimization, 2020, 58(4), 1961-1983

Editorial: Society for Industrial and Applied Mathematics

 Año de publicación: 2020

Nº de páginas: 23

Tipo de publicación: Artículo de Revista

 DOI: 10.1137/19M1293442

ISSN: 0363-0129,1095-7138

Proyecto español: MTM2017-83185-P