论文标题
尖锐半齿问题的超线性收敛亚级别方法
A superlinearly convergent subgradient method for sharp semismooth problems
论文作者
论文摘要
亚级别方法包括基本的非滑动优化算法。经典的结果表明，某些亚速率方法会收敛于一般Lipschitz凸功能的均方根性，并对凸出远离溶液的凸函数进行线性收敛。最近的工作将这些结果扩展到某些非概念问题。在这项工作中，我们试图提高这些算法的复杂性，问：是否有可能设计超线性收敛的亚级别方法？我们为这个问题提供了一个积极的答案，以提供一系列尖锐的半齿功能。
Subgradient methods comprise a fundamental class of nonsmooth optimization algorithms. Classical results show that certain subgradient methods converge sublinearly for general Lipschitz convex functions and converge linearly for convex functions that grow sharply away from solutions. Recent work has moreover extended these results to certain nonconvex problems. In this work we seek to improve the complexity of these algorithms, asking: is it possible to design a superlinearly convergent subgradient method? We provide a positive answer to this question for a broad class of sharp semismooth functions.
