{"title":"凸多边形的最小欧几里德范数点:Wolfe的组合算法是指数型的","authors":"J. D. Loera, Jamie Haddock, Luis Rademacher","doi":"10.1145/3188745.3188820","DOIUrl":null,"url":null,"abstract":"The complexity of Philip Wolfe’s method for the minimum Euclidean-norm point problem over a convex polytope has remained unknown since he proposed the method in 1974. We present the first example that Wolfe’s method takes exponential time. Additionally, we improve previous results to show that linear programming reduces in strongly-polynomial time to the minimum norm point problem over a simplex","PeriodicalId":20593,"journal":{"name":"Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing","volume":"163 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2018-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"The minimum Euclidean-norm point in a convex polytope: Wolfe's combinatorial algorithm is exponential\",\"authors\":\"J. D. Loera, Jamie Haddock, Luis Rademacher\",\"doi\":\"10.1145/3188745.3188820\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The complexity of Philip Wolfe’s method for the minimum Euclidean-norm point problem over a convex polytope has remained unknown since he proposed the method in 1974. We present the first example that Wolfe’s method takes exponential time. Additionally, we improve previous results to show that linear programming reduces in strongly-polynomial time to the minimum norm point problem over a simplex\",\"PeriodicalId\":20593,\"journal\":{\"name\":\"Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing\",\"volume\":\"163 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-06-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3188745.3188820\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3188745.3188820","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 7
摘要
Philip Wolfe的凸多面体上最小欧几里得范数点问题的方法自1974年提出以来，其复杂性一直是未知的。我们给出了Wolfe方法需要指数时间的第一个例子。此外，我们改进了先前的结果，表明线性规划在强多项式时间内减少了单纯形上的最小范数点问题
The minimum Euclidean-norm point in a convex polytope: Wolfe's combinatorial algorithm is exponential
The complexity of Philip Wolfe’s method for the minimum Euclidean-norm point problem over a convex polytope has remained unknown since he proposed the method in 1974. We present the first example that Wolfe’s method takes exponential time. Additionally, we improve previous results to show that linear programming reduces in strongly-polynomial time to the minimum norm point problem over a simplex
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