{"title":"凸集交点上的p范数最小化","authors":"I. Bayram","doi":"10.5281/ZENODO.42790","DOIUrl":null,"url":null,"abstract":"We consider the minimization of the ℓp norm subject to convex constraints. The problem considered in this paper may be regarded as a relaxation of a similar problem that employs the ℓ1 norm. We derive the dual problem, which is unconstrained and devise an algorithm for the dual problem by adapting the Douglas-Rachford algorithm. We demonstrate the utility of the algorithm on an experiment and discuss its differences with an existing algorithm.","PeriodicalId":201182,"journal":{"name":"2012 Proceedings of the 20th European Signal Processing Conference (EUSIPCO)","volume":"12 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2012-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"P-norm minimization over intersections of convex sets\",\"authors\":\"I. Bayram\",\"doi\":\"10.5281/ZENODO.42790\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the minimization of the ℓp norm subject to convex constraints. The problem considered in this paper may be regarded as a relaxation of a similar problem that employs the ℓ1 norm. We derive the dual problem, which is unconstrained and devise an algorithm for the dual problem by adapting the Douglas-Rachford algorithm. We demonstrate the utility of the algorithm on an experiment and discuss its differences with an existing algorithm.\",\"PeriodicalId\":201182,\"journal\":{\"name\":\"2012 Proceedings of the 20th European Signal Processing Conference (EUSIPCO)\",\"volume\":\"12 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-10-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2012 Proceedings of the 20th European Signal Processing Conference (EUSIPCO)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5281/ZENODO.42790\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2012 Proceedings of the 20th European Signal Processing Conference (EUSIPCO)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5281/ZENODO.42790","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
P-norm minimization over intersections of convex sets
We consider the minimization of the ℓp norm subject to convex constraints. The problem considered in this paper may be regarded as a relaxation of a similar problem that employs the ℓ1 norm. We derive the dual problem, which is unconstrained and devise an algorithm for the dual problem by adapting the Douglas-Rachford algorithm. We demonstrate the utility of the algorithm on an experiment and discuss its differences with an existing algorithm.
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