@article{10902/20289,
year = {2020},
url = {http://hdl.handle.net/10902/20289},
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 L0-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.},
organization = {The work of the first author was partially supported by the Spanish Ministerio de Economía y Competitividad under research project MTM2017-83185-P. The work of the second author was partially supported by the German Research Foundation (DFG) under project grant Wa 3626/3-2.},
publisher = {Society for Industrial and Applied Mathematics},
publisher = {SIAM Journal on Control and Optimization, 2020, 58(6), 3486-3507},
title = {First and second order conditions for optimal control problems with an L0 term in the cost functional},
author = {Casas Rentería, Eduardo and Wachsmuth, Daniel},
}