Lipschitz-Free Projected Subgradient Method with Time-Varying Step-Size

Yong Xia; Yan Hao Zhang; Zhi Han Zhu

doi:10.1007/s40305-025-00629-5

Lipschitz-Free Projected Subgradient Method with Time-Varying Step-Size

Yong Xia
, Yan Hao Zhang
, Zhi Han Zhu^*

^*此作品的通讯作者

数学科学学院

Beihang University

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

We introduce a novel family of time-varying step-sizes for the classical projected subgradient method, offering optimal ergodic convergence. Importantly, this approach does not depend on the Lipschitz assumption of the objective function, thereby broadening the convergence result of projected subgradient method to non-Lipschitz case.

源语言	英语
期刊	Journal of the Operations Research Society of China
DOI	https://doi.org/10.1007/s40305-025-00629-5
出版状态	已接受/待刊 - 2025

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10.1007/s40305-025-00629-5

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title = "Lipschitz-Free Projected Subgradient Method with Time-Varying Step-Size",

abstract = "We introduce a novel family of time-varying step-sizes for the classical projected subgradient method, offering optimal ergodic convergence. Importantly, this approach does not depend on the Lipschitz assumption of the objective function, thereby broadening the convergence result of projected subgradient method to non-Lipschitz case.",

keywords = "Nonsmooth convex optimization, Projected subgradient method, Step-size",

author = "Yong Xia and Zhang, \{Yan Hao\} and Zhu, \{Zhi Han\}",

note = "Publisher Copyright: {\textcopyright} Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature 2025.",

year = "2025",

doi = "10.1007/s40305-025-00629-5",

language = "英语",

journal = "Journal of the Operations Research Society of China",

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TY - JOUR

T1 - Lipschitz-Free Projected Subgradient Method with Time-Varying Step-Size

AU - Xia, Yong

AU - Zhang, Yan Hao

AU - Zhu, Zhi Han

N1 - Publisher Copyright: © Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature 2025.

PY - 2025

Y1 - 2025

N2 - We introduce a novel family of time-varying step-sizes for the classical projected subgradient method, offering optimal ergodic convergence. Importantly, this approach does not depend on the Lipschitz assumption of the objective function, thereby broadening the convergence result of projected subgradient method to non-Lipschitz case.

AB - We introduce a novel family of time-varying step-sizes for the classical projected subgradient method, offering optimal ergodic convergence. Importantly, this approach does not depend on the Lipschitz assumption of the objective function, thereby broadening the convergence result of projected subgradient method to non-Lipschitz case.

KW - Nonsmooth convex optimization

KW - Projected subgradient method

KW - Step-size

UR - https://www.scopus.com/pages/publications/105016255768

U2 - 10.1007/s40305-025-00629-5

DO - 10.1007/s40305-025-00629-5

M3 - 文章

AN - SCOPUS:105016255768

SN - 2194-668X

JO - Journal of the Operations Research Society of China

JF - Journal of the Operations Research Society of China

ER -

Lipschitz-Free Projected Subgradient Method with Time-Varying Step-Size

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