论文标题
$ l^0（ω）$约束的最佳控制问题：最大原理和近端梯度方法
Optimal control problems with $L^0(Ω)$ constraints: maximum principle and proximal gradient method
论文作者
论文摘要
我们使用$ L^0 $约束研究最佳控制问题，这限制了对控件的支持的度量。我们证明了最大原理类型的必要最佳条件。在这里，使用特殊的控制扰动，尊重$ l^0 $约束。首先，最大原理以整体形式获得，然后将其变成一个点式形式。另外，分析了近端梯度类型的优化算法。在某些假设下，迭代的序列包含强烈融合的子序列，其极限是可行的，并满足了必要的最佳条件的子集。
We investigate optimal control problems with $L^0$ constraints, which restrict the measure of the support of the controls. We prove necessary optimality conditions of Pontryagin maximum principle type. Here, a special control perturbation is used that respects the $L^0$ constraint. First, the maximum principle is obtained in integral form, which is then turned into a pointwise form. In addition, an optimization algorithm of proximal gradient type is analyzed. Under some assumptions, the sequence of iterates contains strongly converging subsequences, whose limits are feasible and satisfy a subset of the necessary optimality conditions.
