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Moreover, in some cases, analytic formulas are not even available. In this paper, we build upon automatic differentiation and propose a method that, given an implementation of the function to be minimized, efficiently computes Riemannian gradients and matrix-by-vector products between an approximate Riemannian Hessian and a given vector.<\/jats:p>","DOI":"10.1137\/20m1356774","type":"journal-article","created":{"date-parts":[[2022,4,21]],"date-time":"2022-04-21T11:17:43Z","timestamp":1650539863000},"page":"A843-A869","source":"Crossref","is-referenced-by-count":5,"title":["Automatic Differentiation for Riemannian Optimization on Low-Rank Matrix and Tensor-Train Manifolds"],"prefix":"10.1137","volume":"44","author":[{"given":"Alexander","family":"Novikov","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Maxim","family":"Rakhuba","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ivan","family":"Oseledets","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2022,4,21]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-011-0419-7"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1515\/9781400830244"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-40020-9_39"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/15M1032909"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/090764566"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/17M1123080"},{"key":"atypb7","volume-title":"TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems","author":"Abadi M.","year":"2015"},{"key":"atypb8","volume-title":"Tensorly: Tensor Learning in Python, preprint, arXiv:1610.09555","author":"Kossaifi J.","year":"2016"},{"key":"atypb9","volume-title":"TT-Toolbox","author":"Oseledets I. 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