State-constrained semilinear elliptic optimization problems with unrestricted sparse controls

Abstract: In this paper, we consider optimal control problems associated with semilinear elliptic equation equations, where the states are subject to pointwise constraints but there are no explicit constraints on the controls. A term is included in the cost functional promoting the sparsity of the optimal control. We prove existence of optimal controls and derive first and second order optimality conditions. In addition, we establish some regularity results for the optimal controls and the associated adjoint states and Lagrange multipliers.

 Autoría: Casas E., Tröltzsch F.,

 Fuente: Mathematical Control and Related Fields, 2020, 10(3): 527-546

Editorial: American Institute of Mathematical Sciences

 Fecha de publicación: 01/09/2020

Nº de páginas: 20

Tipo de publicación: Artículo de Revista

DOI: 10.3934/mcrf.2020009

ISSN: 2156-8472,2156-8499

Proyecto español: MTM2014-57531-P ; MTM2017-83185-P

Url de la publicación: https://doi.org/10.3934/mcrf.2020009