Analysis of Optimal Control Problems with an $L^0$ Term in the Cost Functional
Optimization and Control
2020-02-13 v1
Abstract
In this paper, we investigate optimal control problems subject to a semilinear elliptic partial differential equations. The cost functional contains a term that measures the size of the support of the control, which is the so-called -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 condition.
Cite
@article{arxiv.2002.04921,
title = {Analysis of Optimal Control Problems with an $L^0$ Term in the Cost Functional},
author = {Eduardo Casas and Daniel Wachsmuth},
journal= {arXiv preprint arXiv:2002.04921},
year = {2020}
}