论文标题
一种用于控制问题的近端梯度方法
A proximal gradient method for control problems with nonsmooth and nonconvex control cost
论文作者
论文摘要
我们研究了近端梯度方法的应用来控制非平滑和非凸控制成本的问题。在这里，我们专注于促进稀疏性的控制成本功能，其中包括$ l^p $ -type的功能，in [0,1）$。我们证明了该方法的弱极限点的平稳性属性。这些属性比Pontryagin的最大原则提供的属性弱，并且比$ L $ stationality弱。
We investigate the convergence of an application of a proximal gradient method to control problems with nonsmooth and nonconvex control cost. Here, we focus on control cost functionals that promote sparsity, which includes functionals of $L^p$-type for $p\in [0,1)$. We prove stationarity properties of weak limit points of the method. These properties are weaker than those provided by Pontryagin's maximum principle and weaker than $L$-stationarity.
