{"title":"Newton's method and the goldstein step length rule for constrained minimization","authors":"J. Dunn","doi":"10.1109/CDC.1980.272011","DOIUrl":null,"url":null,"abstract":"A relaxed form of Newton's method is analyzed for the problem, min¿F, with ¿ a convex subset of a real Banach space X, and F:X ¿ R1 twice differentiable in Fréchet's sense. Feasible directions are obtained by minimizing local quadratic approximations Q to F, and step lengths are determined by Goldstein's rule. The results established here yield two significant extensions of an earlier theorem of Goldstein for the special case ¿ = X = a Hilbert space. Connections are made with a recently formulated classification scheme for singular and nonsingular extremals.","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"65 ","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1980-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.1980.272011","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
A relaxed form of Newton's method is analyzed for the problem, min¿F, with ¿ a convex subset of a real Banach space X, and F:X ¿ R1 twice differentiable in Fréchet's sense. Feasible directions are obtained by minimizing local quadratic approximations Q to F, and step lengths are determined by Goldstein's rule. The results established here yield two significant extensions of an earlier theorem of Goldstein for the special case ¿ = X = a Hilbert space. Connections are made with a recently formulated classification scheme for singular and nonsingular extremals.
对于具有实Banach空间X的凸子集，且F:X¿R1在frimcheet意义上可二阶微的min¿F问题，本文分析了牛顿方法的一种松弛形式。通过最小化局部二次逼近Q到F得到可行方向，步长由Goldstein规则确定。这里建立的结果对特殊情况¿= X = a Hilbert空间给出了Goldstein早期定理的两个重要推广。连接与最近制定的奇异和非奇异极值的分类方案。
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
