{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:43:47Z","timestamp":1787341427208,"version":"build-2736575974"},"reference-count":16,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>Gouveia, Parrilo, and Thomas gave a description of certain rank functions of matrices in geometric terms, generalizing a celebrated result of Yannakakis on the nonnegative rank. We analyze the algorithmic complexity of their description using the results of Renegar on the first-order theory of the reals. This gives a proof that matrices whose positive semidefinite rank is equal to an integer fixed in advance can be detected in polynomial time.<\/jats:p>","DOI":"10.1137\/17m1141345","type":"journal-article","created":{"date-parts":[[2018,7,24]],"date-time":"2018-07-24T13:45:04Z","timestamp":1532439904000},"page":"2067-2072","source":"Crossref","is-referenced-by-count":3,"title":["Matrices of Bounded Psd Rank are Easy to Detect"],"prefix":"10.1137","volume":"28","author":[{"given":"Yaroslav","family":"Shitov","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,7,24]]},"reference":[{"key":"atypb1","first-page":"145","author":"Arora S.","year":"2012","journal-title":"New York"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-1989-15750-9"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-015-0922-1"},{"key":"atypb4","first-page":"95","author":"Fiorini S.","year":"2012","journal-title":"New York"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1120.0575"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-015-0867-4"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2016.08.002"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1137\/0222067"},{"key":"atypb9","first-page":"567","author":"Lee J. R.","year":"2015","journal-title":"New York"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1137\/140990139"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/S0747-7171(10)80005-7"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/16M1080616"},{"key":"atypb13","unstructured":"Y. Shitov,\n                      A Universality Theorem for Nonnegative Matrix Factorizations\n                      , preprint,https:\/\/arxiv.org\/abs\/1606.09068, 2016."},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/16M1080999"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1137\/070709967"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(91)90024-Y"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/17M1141345","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:18:48Z","timestamp":1787339928000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/17M1141345"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":16,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/17M1141345"],"URL":"https:\/\/doi.org\/10.1137\/17m1141345","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}