{"title":"一致凸巴拿赫空间变分不等式算子外推法的弱收敛性","authors":"S. Denisov, V. Semenov, O. Kharkov","doi":"10.17721/2706-9699.2022.2.05","DOIUrl":null,"url":null,"abstract":"This work is devoted to the study of new iterative algorithms for solving variational inequalities in uniformly convex Banach spaces. The first algorithm is a modification of the forward-reflectedbackward algorithm, which uses the Alber generalized projection instead of the metric one. The second algorithm is an adaptive version of the first one, where the monotone step size update rule is used, which does not require knowledge of Lipschitz constants and linear search procedure.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"165 1","pages":""},"PeriodicalIF":0.1000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"WEAK CONVERGENCE OF THE OPERATOR EXTRAPOLATION METHOD FOR VARIATIONAL INEQUALITIES IN UNIFORMLY CONVEX BANACH SPACES\",\"authors\":\"S. Denisov, V. Semenov, O. Kharkov\",\"doi\":\"10.17721/2706-9699.2022.2.05\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This work is devoted to the study of new iterative algorithms for solving variational inequalities in uniformly convex Banach spaces. The first algorithm is a modification of the forward-reflectedbackward algorithm, which uses the Alber generalized projection instead of the metric one. The second algorithm is an adaptive version of the first one, where the monotone step size update rule is used, which does not require knowledge of Lipschitz constants and linear search procedure.\",\"PeriodicalId\":40347,\"journal\":{\"name\":\"Journal of Numerical and Applied Mathematics\",\"volume\":\"165 1\",\"pages\":\"\"},\"PeriodicalIF\":0.1000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Numerical and Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17721/2706-9699.2022.2.05\",\"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/10.17721/2706-9699.2022.2.05","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
WEAK CONVERGENCE OF THE OPERATOR EXTRAPOLATION METHOD FOR VARIATIONAL INEQUALITIES IN UNIFORMLY CONVEX BANACH SPACES
This work is devoted to the study of new iterative algorithms for solving variational inequalities in uniformly convex Banach spaces. The first algorithm is a modification of the forward-reflectedbackward algorithm, which uses the Alber generalized projection instead of the metric one. The second algorithm is an adaptive version of the first one, where the monotone step size update rule is used, which does not require knowledge of Lipschitz constants and linear search procedure.
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