论文标题
成本功能中的$ l^0 $项的最佳控制问题分析
Analysis of Optimal Control Problems with an $L^0$ Term in the Cost Functional
论文作者
论文摘要
在本文中，我们研究了受半椭圆形偏微分方程的最佳控制问题。成本功能包含一个术语，该术语可以测量控件支持的大小，即所谓的$ l^0 $ -Norm。我们提供二阶的必要最佳条件。通过分析部分共汇的问题获得了足够的二阶条件。有趣的是，问题的结构产生了二阶条件，具有不同的双线性形式，以适应足够的条件。
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 $L^0$-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 condition.
