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First and second order conditions for optimal control problems with an $L^0$ term in the cost functional

Abstract: In this paper, we investigate optimal control problems subject to a semilinear elliptic partial differential equation. The cost functional contains a term that measures the size of the support of the control, which is the so-called $L^0$-norm. We provide necessary and sufficient optimality conditions of second order. The sufficient second-order condition is obtained by analyzing a partially convexified problem. Interestingly, the structure of the problem yields second-order conditions with different bilinear forms for the necessary and for the sufficient conditions

 Autoría: Casas E., Wachsmuth D.,

 Fuente: SIAM Journal on Control and Optimization, 2020, 58(6), 3486-3507

 Editorial: Society for Industrial and Applied Mathematics

 Año de publicación: 2020

 Nº de páginas: 22

 Tipo de publicación: Artículo de Revista

 DOI: 10.1137/20M1318377

 ISSN: 0363-0129,1095-7138

 Proyecto español: MTM2017-83185-P