Convergence rate of projected subgradient method with time-varying step-sizes

Zhihan Zhu; Yanhao Zhang; Yong Xia

doi:10.1007/s11590-024-02142-9

Convergence rate of projected subgradient method with time-varying step-sizes

Zhihan Zhu
, Yanhao Zhang
, Yong Xia^*

^*Corresponding author for this work

School of Mathematical Sciences

Beihang University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We establish the optimal ergodic convergence rate for the classical projected subgradient method with time-varying step-sizes. This convergence rate remains the same even if we slightly increase the weight of the most recent points, thereby relaxing the ergodic sense.

Original language	English
Pages (from-to)	1027-1031
Number of pages	5
Journal	Optimization Letters
Volume	19
Issue number	5
DOIs	https://doi.org/10.1007/s11590-024-02142-9
State	Published - Jun 2025

Keywords

Ergodic convergence rate
Nonsmooth convex optimization
Step-size
Subgradient method

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10.1007/s11590-024-02142-9

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title = "Convergence rate of projected subgradient method with time-varying step-sizes",

abstract = "We establish the optimal ergodic convergence rate for the classical projected subgradient method with time-varying step-sizes. This convergence rate remains the same even if we slightly increase the weight of the most recent points, thereby relaxing the ergodic sense.",

keywords = "Ergodic convergence rate, Nonsmooth convex optimization, Step-size, Subgradient method",

author = "Zhihan Zhu and Yanhao Zhang and Yong Xia",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.",

year = "2025",

month = jun,

doi = "10.1007/s11590-024-02142-9",

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T1 - Convergence rate of projected subgradient method with time-varying step-sizes

AU - Zhu, Zhihan

AU - Zhang, Yanhao

AU - Xia, Yong

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.

PY - 2025/6

Y1 - 2025/6

N2 - We establish the optimal ergodic convergence rate for the classical projected subgradient method with time-varying step-sizes. This convergence rate remains the same even if we slightly increase the weight of the most recent points, thereby relaxing the ergodic sense.

AB - We establish the optimal ergodic convergence rate for the classical projected subgradient method with time-varying step-sizes. This convergence rate remains the same even if we slightly increase the weight of the most recent points, thereby relaxing the ergodic sense.

KW - Ergodic convergence rate

KW - Nonsmooth convex optimization

KW - Step-size

KW - Subgradient method

UR - https://www.scopus.com/pages/publications/85200970662

U2 - 10.1007/s11590-024-02142-9

DO - 10.1007/s11590-024-02142-9

M3 - 文章

AN - SCOPUS:85200970662

SN - 1862-4472

VL - 19

SP - 1027

EP - 1031

JO - Optimization Letters

JF - Optimization Letters

IS - 5

ER -

Convergence rate of projected subgradient method with time-varying step-sizes

Abstract

Keywords

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