论文标题
Lipschitz路径可区分功能的亚级别方法的长期动力学
Long term dynamics of the subgradient method for Lipschitz path differentiable functions
论文作者
论文摘要
在目标函数既不光滑也不是凸的情况下，我们考虑消失的步骤尺寸亚级别方法的长期动力学。我们假设此功能是局部Lipschitz，并且路径可区分，即接受链条规则。我们的研究偏离了其他作品，从某种意义上说，我们专注于振荡的行为，为此，我们采用了封闭的措施。我们恢复已知的收敛结果，建立新的收敛结果，并显示了速度的局部原理。粗略地说，一个限制点左右的梯度的平均时间消失了。这使我们能够进一步分析振荡的结构，并确定其对一般漂移的垂直性。
We consider the long-term dynamics of the vanishing stepsize subgradient method in the case when the objective function is neither smooth nor convex. We assume that this function is locally Lipschitz and path differentiable, i.e., admits a chain rule. Our study departs from other works in the sense that we focus on the behavoir of the oscillations, and to do this we use closed measures. We recover known convergence results, establish new ones, and show a local principle of oscillation compensation for the velocities. Roughly speaking, the time average of gradients around one limit point vanishes. This allows us to further analyze the structure of oscillations, and establish their perpendicularity to the general drift.
