论文标题
整数最佳控制问题与总变化正则化：最佳条件和子问题的快速解决方案
Integer optimal control problems with total variation regularization: Optimality conditions and fast solution of subproblems
论文作者
论文摘要
我们通过有限维切换点问题研究了整数最佳控制问题的第一和二阶的局部最佳条件，并研究了总变化正则化。我们显示了两个问题的局部最优性等效性，这些问题将用于得出有关控制功能的切换点的条件。将制定来回处理的非本地最佳条件。 对于数值解决方案，我们提出了一种近端梯度方法。新兴的离散子问题将通过采用Bellman的最佳原理来解决，从而导致算法在网格大小和可允许的控制级别中是多项式的算法。该算法的适应性可用于处理2021年Leyffer，Manns Leyffer提出的信任区域的子问题。最后，我们演示了计算结果。
We investigate local optimality conditions of first and second order for integer optimal control problems with total variation regularization via a finite-dimensional switching point problem. We show the equivalence of local optimality for both problems, which will be used to derive conditions concerning the switching points of the control function. A non-local optimality condition treating back-and-forth switches will be formulated. For the numerical solution, we propose a proximal-gradient method. The emerging discretized subproblems will be solved by employing Bellman's optimality principle, leading to an algorithm which is polynomial in the mesh size and in the admissible control levels. An adaption of this algorithm can be used to handle subproblems of the trust-region method proposed in Leyffer, Manns, 2021. Finally, we demonstrate computational results.
