{"title":"非光滑变分问题解的表征及对偶性","authors":"Juan Zhang, Changzhao Li","doi":"10.5281/ZENODO.1088172","DOIUrl":null,"url":null,"abstract":"In this paper, we introduce a new class of nonsmooth pseudo-invex and nonsmooth quasi-invex functions to non-smooth variational problems. By using these concepts, numbers of necessary and sufficient conditions are established for a nonsmooth variational problem wherein Clarke’s generalized gradient is used. Also, weak, strong and converse duality are established. Keywords—Variational problem; Nonsmooth pseudo-invex; Nonsmooth quasi-invex; Critical point; Duality","PeriodicalId":23764,"journal":{"name":"World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering","volume":"23 1","pages":"112-118"},"PeriodicalIF":0.0000,"publicationDate":"2013-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Characterization of Solutions of Nonsmooth Variational Problems and Duality\",\"authors\":\"Juan Zhang, Changzhao Li\",\"doi\":\"10.5281/ZENODO.1088172\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we introduce a new class of nonsmooth pseudo-invex and nonsmooth quasi-invex functions to non-smooth variational problems. By using these concepts, numbers of necessary and sufficient conditions are established for a nonsmooth variational problem wherein Clarke’s generalized gradient is used. Also, weak, strong and converse duality are established. Keywords—Variational problem; Nonsmooth pseudo-invex; Nonsmooth quasi-invex; Critical point; Duality\",\"PeriodicalId\":23764,\"journal\":{\"name\":\"World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering\",\"volume\":\"23 1\",\"pages\":\"112-118\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-09-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5281/ZENODO.1088172\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5281/ZENODO.1088172","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Characterization of Solutions of Nonsmooth Variational Problems and Duality
In this paper, we introduce a new class of nonsmooth pseudo-invex and nonsmooth quasi-invex functions to non-smooth variational problems. By using these concepts, numbers of necessary and sufficient conditions are established for a nonsmooth variational problem wherein Clarke’s generalized gradient is used. Also, weak, strong and converse duality are established. Keywords—Variational problem; Nonsmooth pseudo-invex; Nonsmooth quasi-invex; Critical point; Duality
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
