论文标题
在梯度采样方法中使用二阶信息进行非平滑优化
Using second-order information in gradient sampling methods for nonsmooth optimization
论文作者
论文摘要
在本文中，我们介绍了一个新颖的概念，以供受到Goldstein Eps-Subdferention启发的非平滑函数的二阶信息。它包括在给定点附近的EPS球中所有现有二阶泰勒膨胀的系数。基于这个概念，我们将目标模型定义为这些泰勒膨胀的最大值，并在实践中得出了一个采样方案。该模型的最小化诱导了一种简单的下降方法，为此，我们显示了物镜为凸或最大型的情况。虽然我们没有证明这种方法的收敛速度，但数值实验表明，相对于目标呼叫的数量，超线性行为。
In this article, we introduce a novel concept for second-order information of a nonsmooth function inspired by the Goldstein eps-subdifferential. It comprises the coefficients of all existing second-order Taylor expansions in an eps-ball around a given point. Based on this concept, we define a model of the objective as the maximum of these Taylor expansions, and derive a sampling scheme for its approximation in practice. Minimization of this model induces a simple descent method, for which we show convergence for the case where the objective is convex or of max-type. While we do not prove any rate of convergence of this method, numerical experiments suggest superlinear behavior with respect to the number of oracle calls of the objective.
