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首页> 外文期刊>IEEE Signal Processing Magazine >Understanding Notions of Stationarity in Nonsmooth Optimization: A Guided Tour of Various Constructions of Subdifferential for Nonsmooth Functions
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Understanding Notions of Stationarity in Nonsmooth Optimization: A Guided Tour of Various Constructions of Subdifferential for Nonsmooth Functions

机译：了解非光滑优化中的实体性概念：用于非光驱的各种结构的导游

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摘要

Many contemporary applications in signal processing and machine learning give rise to structured nonconvex nonsmooth optimization problems that can often be tackled by simple iterative methods quite effectively. One of the keys to understanding such a phenomenon-and, in fact, a very difficult conundrum even for experts-lies in the study of "stationary points" of the problem in question. Unlike smooth optimization, for which the definition of a stationary point is rather standard, there are myriad definitions of stationarity in nonsmooth optimization. In this article, we provide an introduction to different stationarity concepts for several important classes of nonconvex nonsmooth functions, discuss the geometric interpretations of these concepts, and further clarify their relationships. We then demonstrate the relevance of these constructions in some representative applications and indicate how they could affect the performance of iterative methods for addressing these applications.
机译：信号处理和机器学习中的许多当代应用导致结构化的非凸起的非光学优化问题，这些问题通常会非常有效地通过简单的迭代方法解决。理解这种现象的钥匙之一 - 事实上，即使是专家们也是非常困难的难题 - 在于研究有关问题的“静止点”的研究。与顺利优化不同，静止点的定义是相当标准的，在非光学优化中存在具有实质性的Myriad定义。在本文中，我们为几个重要的非谐波非函数类别提供了不同的实体概念，讨论了这些概念的几何解释，并进一步阐明了他们的关系。然后，我们展示了这些构造在一些代表性应用中的相关性，并指出它们如何影响解决这些应用程序的迭代方法的性能。

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