{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T15:32:57Z","timestamp":1770564777800,"version":"3.49.0"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,11,13]],"date-time":"2021-11-13T00:00:00Z","timestamp":1636761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,11,13]],"date-time":"2021-11-13T00:00:00Z","timestamp":1636761600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2022,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The low-rank matrix completion problem can be solved by Riemannian optimization on a fixed-rank manifold. However, a drawback of the known approaches is that the rank parameter has to be fixed a priori. In this paper, we consider the optimization problem on the set of bounded-rank matrices. We propose a Riemannian rank-adaptive method, which consists of fixed-rank optimization, rank increase step and rank reduction step. We explore its performance applied to the low-rank matrix completion problem. Numerical experiments on synthetic and real-world datasets illustrate that the proposed rank-adaptive method compares favorably with state-of-the-art algorithms. In addition, it shows that one can incorporate each aspect of this rank-adaptive framework separately into existing algorithms for the purpose of improving performance.<\/jats:p>","DOI":"10.1007\/s10589-021-00328-w","type":"journal-article","created":{"date-parts":[[2021,11,13]],"date-time":"2021-11-13T03:02:20Z","timestamp":1636772540000},"page":"67-90","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":33,"title":["A Riemannian rank-adaptive method for low-rank matrix completion"],"prefix":"10.1007","volume":"81","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5290-4675","authenticated-orcid":false,"given":"Bin","family":"Gao","sequence":"first","affiliation":[]},{"given":"P.-A.","family":"Absil","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,11,13]]},"reference":[{"key":"328_CR1","doi-asserted-by":"publisher","DOI":"10.1515\/9781400830244","volume-title":"Optimization Algorithms on Matrix Manifolds","author":"P-A Absil","year":"2008","unstructured":"Absil, P.-A., Mahony, R., Sepulchre, R.: Optimization Algorithms on Matrix Manifolds. 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