{"title":"具有随机子空间的两级信任区域法","authors":"Andrea Angino, Alena Kopaničáková, Rolf Krause","doi":"arxiv-2409.05479","DOIUrl":null,"url":null,"abstract":"We introduce a two-level trust-region method (TLTR) for solving unconstrained\nnonlinear optimization problems. Our method uses a composite iteration step,\nwhich is based on two distinct search directions. The first search direction is\nobtained through minimization in the full/high-resolution space, ensuring\nglobal convergence to a critical point. The second search direction is obtained\nthrough minimization in the randomly generated subspace, which, in turn, allows\nfor convergence acceleration. The efficiency of the proposed TLTR method is\ndemonstrated through numerical experiments in the field of machine learning","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"50 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Two-level trust-region method with random subspaces\",\"authors\":\"Andrea Angino, Alena Kopaničáková, Rolf Krause\",\"doi\":\"arxiv-2409.05479\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce a two-level trust-region method (TLTR) for solving unconstrained\\nnonlinear optimization problems. Our method uses a composite iteration step,\\nwhich is based on two distinct search directions. The first search direction is\\nobtained through minimization in the full/high-resolution space, ensuring\\nglobal convergence to a critical point. The second search direction is obtained\\nthrough minimization in the randomly generated subspace, which, in turn, allows\\nfor convergence acceleration. The efficiency of the proposed TLTR method is\\ndemonstrated through numerical experiments in the field of machine learning\",\"PeriodicalId\":501162,\"journal\":{\"name\":\"arXiv - MATH - Numerical Analysis\",\"volume\":\"50 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Numerical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.05479\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.05479","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Two-level trust-region method with random subspaces
We introduce a two-level trust-region method (TLTR) for solving unconstrained
nonlinear optimization problems. Our method uses a composite iteration step,
which is based on two distinct search directions. The first search direction is
obtained through minimization in the full/high-resolution space, ensuring
global convergence to a critical point. The second search direction is obtained
through minimization in the randomly generated subspace, which, in turn, allows
for convergence acceleration. The efficiency of the proposed TLTR method is
demonstrated through numerical experiments in the field of machine learning