Scholarlink

<p>In this work, we develop new regularity conditions in nonsmooth analysis that parallel the stratification conditions of Whitney, Kuo, and Verdier. They quantify how subgradients interact with a certain “active manifold” that captures the nonsmooth activity of the function. Based on these new conditions, we show that several subgradient-based methods converge only to local minimizers when applied to generic Lipschitz and subdifferentially regular functions that are definable in an o-minimal structure. At a high level, our argument is appealingly transparent: we interpret the nonsmooth dynamics as an approximate Riemannian gradient method on the active manifold. As a by-product, we extend the stochastic processes techniques of Pemantle.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Active Manifolds, Stratifications, and Convergence to Local Minima in Nonsmooth Optimization

  • 期刊论文

  • 发表日期：

    2025年1月22日

查看全文
  • Damek Davis,
  • Dmitriy Drusvyatskiy,
  • Liwei Jiang

摘要

In this work, we develop new regularity conditions in nonsmooth analysis that parallel the stratification conditions of Whitney, Kuo, and Verdier. They quantify how subgradients interact with a certain “active manifold” that captures the nonsmooth activity of the function. Based on these new conditions, we show that several subgradient-based methods converge only to local minimizers when applied to generic Lipschitz and subdifferentially regular functions that are definable in an o-minimal structure. At a high level, our argument is appealingly transparent: we interpret the nonsmooth dynamics as an approximate Riemannian gradient method on the active manifold. As a by-product, we extend the stochastic processes techniques of Pemantle.