标题： 重新审视几何衰减步长：光滑或非光滑函数的线性收敛 显示英文标题

标题： Revisiting the Geometrically Decaying Step Size: Linear Convergence for Smooth or Non-Smooth Functions

摘要： 我们重新审视在正条件数下的几何衰减步长，此时局部Lipschitz函数表现出线性收敛性。 正性不要求函数满足凸性、弱凸性、拟凸性或尖锐性，而是比现有工作中使用的假设更弱的性质。 我们提出一种简洁简单的次梯度下降算法，该算法需要最少的问题常数知识，适用于光滑或非光滑函数。 显示英文摘要

摘要： We revisit the geometrically decaying step size given a positive condition number, under which a locally Lipschitz function shows linear convergence. The positivity does not require the function to satisfy convexity, weak convexity, quasar convexity, or sharpness, but instead amounts to a property strictly weaker than the assumptions used in existing works. We propose a clean and simple subgradient descent algorithm that requires minimal knowledge of problem constants, applicable to either smooth or non-smooth functions.