{"title":"具有时变步长的投影子梯度法的收敛率","authors":"Zhihan Zhu, Yanhao Zhang, Yong Xia","doi":"10.1007/s11590-024-02142-9","DOIUrl":null,"url":null,"abstract":"<p>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.</p>","PeriodicalId":49720,"journal":{"name":"Optimization Letters","volume":"120 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Convergence rate of projected subgradient method with time-varying step-sizes\",\"authors\":\"Zhihan Zhu, Yanhao Zhang, Yong Xia\",\"doi\":\"10.1007/s11590-024-02142-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>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.</p>\",\"PeriodicalId\":49720,\"journal\":{\"name\":\"Optimization Letters\",\"volume\":\"120 1\",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-08-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Optimization Letters\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11590-024-02142-9\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Optimization Letters","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11590-024-02142-9","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Convergence rate of projected subgradient method with time-varying step-sizes
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.
期刊介绍：
Optimization Letters is an international journal covering all aspects of optimization, including theory, algorithms, computational studies, and applications, and providing an outlet for rapid publication of short communications in the field. Originality, significance, quality and clarity are the essential criteria for choosing the material to be published.
Optimization Letters has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time one of the most striking trends in optimization is the constantly increasing interdisciplinary nature of the field.
Optimization Letters aims to communicate in a timely fashion all recent developments in optimization with concise short articles (limited to a total of ten journal pages). Such concise articles will be easily accessible by readers working in any aspects of optimization and wish to be informed of recent developments.
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