论文标题
在整数最佳控制上，多维域上具有总变化正则化
On Integer Optimal Control with Total Variation Regularization on Multi-dimensional Domains
论文作者
论文摘要
我们考虑具有整数值控制的最佳控制问题，并考虑二维范围或更高范围的目标的总变化正则惩罚。可行集合在弱的-$^*$中依次关闭的惩罚产量，并在有限变化的功能空间中以严格的拓扑结束。 反过来，我们使用可行控制功能的级别集合的局部变化来得出最佳控制问题的一阶最佳条件以及具有部分线性化模型函数的信任区域子问题。我们还证明，最近提出的函数空间信任区域算法（顺序线性整数编程）会产生其限制为一阶最佳点的迭代序列。
We consider optimal control problems with integer-valued controls and a total variation regularization penalty in the objective on domains of dimension two or higher. The penalty yields that the feasible set is sequentially closed in the weak-$^*$ and closed in the strict topology in the space of functions of bounded variation. In turn, we derive first-order optimality conditions of the optimal control problem as well as trust-region subproblems with partially linearized model functions using local variations of the level sets of the feasible control functions. We also prove that a recently proposed function space trust-region algorithm -- sequential linear integer programming -- produces sequences of iterates whose limits are first-order optimal points.
