具有q度不确切oracle的复合优化近端梯度法

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-04-30 DOI:10.1007/s11590-024-02118-9
Yassine Nabou, François Glineur, Ion Necoara
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引用次数: 0

摘要

我们为一个可能非凸和非光滑函数引入了度数为 q 的非精确一阶甲骨文概念,它自然出现在近似梯度、弱光滑度水平和其他情况下。我们的定义没有现有文献中的定义那么保守,可以看作是完全精确一阶甲骨文定义和现有非精确一阶甲骨文定义之间的一个插值。我们分析了使用这种oracle求解(非)凸复合最小化问题的(快速)不完全近似梯度法的收敛行为。我们得出了复杂性估计值,并研究了oracle 的精度与梯度或目标函数的期望精度之间的依赖关系。我们的结果表明,当 q 较大时,在理论上和数值模拟中都能获得更好的计算率。
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Proximal gradient methods with inexact oracle of degree q for composite optimization

We introduce the concept of inexact first-order oracle of degree q for a possibly nonconvex and nonsmooth function, which naturally appears in the context of approximate gradient, weak level of smoothness and other situations. Our definition is less conservative than those found in the existing literature, and it can be viewed as an interpolation between fully exact and the existing inexact first-order oracle definitions. We analyze the convergence behavior of a (fast) inexact proximal gradient method using such an oracle for solving (non)convex composite minimization problems. We derive complexity estimates and study the dependence between the accuracy of the oracle and the desired accuracy of the gradient or of the objective function. Our results show that better rates can be obtained both theoretically and in numerical simulations when q is large.

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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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