{"title":"类梯度动力系统的收敛性","authors":"A. Y. Shavlyuk, V. Semenov","doi":"10.17721/2706-9699.2022.1.09","DOIUrl":null,"url":null,"abstract":"The asymptotic behavior of the gradient system, which is a continuous analogue of the variant of the gradient method from [16] for the minimization of strongly convex functions, is studied. Using the Lyapunov analysis, estimates of the rate of convergence of the gradient system were established.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"131 1","pages":""},"PeriodicalIF":0.1000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"CONVERGENCE OF GRADIENT-LIKE DYNAMICAL SYSTEM\",\"authors\":\"A. Y. Shavlyuk, V. Semenov\",\"doi\":\"10.17721/2706-9699.2022.1.09\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The asymptotic behavior of the gradient system, which is a continuous analogue of the variant of the gradient method from [16] for the minimization of strongly convex functions, is studied. Using the Lyapunov analysis, estimates of the rate of convergence of the gradient system were established.\",\"PeriodicalId\":40347,\"journal\":{\"name\":\"Journal of Numerical and Applied Mathematics\",\"volume\":\"131 1\",\"pages\":\"\"},\"PeriodicalIF\":0.1000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Numerical and Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17721/2706-9699.2022.1.09\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Numerical and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17721/2706-9699.2022.1.09","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The asymptotic behavior of the gradient system, which is a continuous analogue of the variant of the gradient method from [16] for the minimization of strongly convex functions, is studied. Using the Lyapunov analysis, estimates of the rate of convergence of the gradient system were established.
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