{"title":"非光滑凸优化问题的共轭梯度算法","authors":"Yaping Hu, Liying Liu, Yujie Wang","doi":"10.19139/soic-2310-5070-908","DOIUrl":null,"url":null,"abstract":"This paper presents a Wei-Yao-Liu conjugate gradient algorithm for nonsmooth convex optimization problem. The proposed algorithm makes use of approximate function and gradient values of the Moreau-Yosida regularization function instead of the corresponding exact values. Under suitable conditions, the global convergence property could be established for the proposed conjugate gradient method. Finally, some numerical results are reported to show the efficiency of our algorithm.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"403-413"},"PeriodicalIF":0.0000,"publicationDate":"2020-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Wei-Yao-Liu Conjugate Gradient Algorithm for Nonsmooth Convex Optimization Problems\",\"authors\":\"Yaping Hu, Liying Liu, Yujie Wang\",\"doi\":\"10.19139/soic-2310-5070-908\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper presents a Wei-Yao-Liu conjugate gradient algorithm for nonsmooth convex optimization problem. The proposed algorithm makes use of approximate function and gradient values of the Moreau-Yosida regularization function instead of the corresponding exact values. Under suitable conditions, the global convergence property could be established for the proposed conjugate gradient method. Finally, some numerical results are reported to show the efficiency of our algorithm.\",\"PeriodicalId\":93376,\"journal\":{\"name\":\"Statistics, optimization & information computing\",\"volume\":\"8 1\",\"pages\":\"403-413\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-05-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Statistics, optimization & information computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.19139/soic-2310-5070-908\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistics, optimization & information computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.19139/soic-2310-5070-908","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Wei-Yao-Liu Conjugate Gradient Algorithm for Nonsmooth Convex Optimization Problems
This paper presents a Wei-Yao-Liu conjugate gradient algorithm for nonsmooth convex optimization problem. The proposed algorithm makes use of approximate function and gradient values of the Moreau-Yosida regularization function instead of the corresponding exact values. Under suitable conditions, the global convergence property could be established for the proposed conjugate gradient method. Finally, some numerical results are reported to show the efficiency of our algorithm.
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