{"title":"凸凹极大极小问题的Korpelevich和Popov超梯度算法的步长选择","authors":"Jiaojiao Wang, H. Xu","doi":"10.37193/cjm.2023.01.22","DOIUrl":null,"url":null,"abstract":"\"We show that the choice of stepsize in Korpelevich's extragradient algorithm is sharp, while the choice of stepsize in Popov's extragradient algorithm can be relaxed. We also extend Korpelevich's extragradient algorithm and Popov's extragradient algorithm (with larger stepsize) to the infinite-dimensional Hilbert space framework, with weak convergence.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stepsize Choice for Korpelevich's and Popov's Extragradient Algorithms for Convex-Concave Minimax Problems\",\"authors\":\"Jiaojiao Wang, H. Xu\",\"doi\":\"10.37193/cjm.2023.01.22\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\\"We show that the choice of stepsize in Korpelevich's extragradient algorithm is sharp, while the choice of stepsize in Popov's extragradient algorithm can be relaxed. We also extend Korpelevich's extragradient algorithm and Popov's extragradient algorithm (with larger stepsize) to the infinite-dimensional Hilbert space framework, with weak convergence.\\\"\",\"PeriodicalId\":50711,\"journal\":{\"name\":\"Carpathian Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2022-07-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Carpathian Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.37193/cjm.2023.01.22\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Carpathian Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.37193/cjm.2023.01.22","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Stepsize Choice for Korpelevich's and Popov's Extragradient Algorithms for Convex-Concave Minimax Problems
"We show that the choice of stepsize in Korpelevich's extragradient algorithm is sharp, while the choice of stepsize in Popov's extragradient algorithm can be relaxed. We also extend Korpelevich's extragradient algorithm and Popov's extragradient algorithm (with larger stepsize) to the infinite-dimensional Hilbert space framework, with weak convergence."
期刊介绍：
Carpathian Journal of Mathematics publishes high quality original research papers and survey articles in all areas of pure and applied mathematics. It will also occasionally publish, as special issues, proceedings of international conferences, generally (co)-organized by the Department of Mathematics and Computer Science, North University Center at Baia Mare. There is no fee for the published papers but the journal offers an Open Access Option to interested contributors.
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