{"title":"变电平干扰条件下梯度法的收敛性","authors":"S.K. Zavriev","doi":"10.1016/0041-5553(90)90040-Y","DOIUrl":null,"url":null,"abstract":"<div><p>The method of steepest gradient descent is considered on the assumption that the values of the objective function and its gradients are computed inaccurately. The limit set of the trajectories of the method is determined. For some types of noise this set cannot be made smaller for any problem of the class under consideration.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 4","pages":"Pages 24-32"},"PeriodicalIF":0.0000,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0041-5553(90)90040-Y","citationCount":"4","resultStr":"{\"title\":\"Convergence properties of the gradient method under conditions of variable-level interference\",\"authors\":\"S.K. Zavriev\",\"doi\":\"10.1016/0041-5553(90)90040-Y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The method of steepest gradient descent is considered on the assumption that the values of the objective function and its gradients are computed inaccurately. The limit set of the trajectories of the method is determined. For some types of noise this set cannot be made smaller for any problem of the class under consideration.</p></div>\",\"PeriodicalId\":101271,\"journal\":{\"name\":\"USSR Computational Mathematics and Mathematical Physics\",\"volume\":\"30 4\",\"pages\":\"Pages 24-32\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1990-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/0041-5553(90)90040-Y\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"USSR Computational Mathematics and Mathematical Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/004155539090040Y\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"USSR Computational Mathematics and Mathematical Physics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/004155539090040Y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Convergence properties of the gradient method under conditions of variable-level interference
The method of steepest gradient descent is considered on the assumption that the values of the objective function and its gradients are computed inaccurately. The limit set of the trajectories of the method is determined. For some types of noise this set cannot be made smaller for any problem of the class under consideration.
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