{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T08:55:35Z","timestamp":1775552135159,"version":"3.50.1"},"reference-count":28,"publisher":"Informa UK Limited","issue":"5","license":[{"start":{"date-parts":[[2024,9,2]],"date-time":"2024-09-02T00:00:00Z","timestamp":1725235200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["21H03398"],"award-info":[{"award-number":["21H03398"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["JP19K20217"],"award-info":[{"award-number":["JP19K20217"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["JP23K16844"],"award-info":[{"award-number":["JP23K16844"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["JP17K00031"],"award-info":[{"award-number":["JP17K00031"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["JP20H04145"],"award-info":[{"award-number":["JP20H04145"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["22H00510"],"award-info":[{"award-number":["22H00510"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["JP20K19748"],"award-info":[{"award-number":["JP20K19748"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["20H04145"],"award-info":[{"award-number":["20H04145"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.tandfonline.com"],"crossmark-restriction":true},"short-container-title":["Optimization Methods and Software"],"published-print":{"date-parts":[[2024,9,2]]},"DOI":"10.1080\/10556788.2024.2409710","type":"journal-article","created":{"date-parts":[[2024,11,8]],"date-time":"2024-11-08T12:43:34Z","timestamp":1731069814000},"page":"1040-1067","update-policy":"https:\/\/doi.org\/10.1080\/tandf_crossmark_01","source":"Crossref","is-referenced-by-count":0,"title":["Closing duality gaps of SDPs completely through perturbation when singularity degree is one"],"prefix":"10.1080","volume":"39","author":[{"given":"Takashi","family":"Tsuchiya","sequence":"first","affiliation":[{"name":"National Graduate Institute for Policy Studies","place":["Minato-ku, Japan"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bruno F.","family":"Louren\u00e7o","sequence":"additional","affiliation":[{"name":"The Institute of Statistical Mathematics","place":["Tachikawa, Japan"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Masakazu","family":"Muramatsu","sequence":"additional","affiliation":[{"name":"The University of Electro-Communications","place":["Chofu, Japan"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Takayuki","family":"Okuno","sequence":"additional","affiliation":[{"name":"Seikei University","place":["Musashino, Japan"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"301","published-online":{"date-parts":[[2024,11,8]]},"reference":[{"key":"e_1_3_4_2_1","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1975.57.15"},{"key":"e_1_3_4_3_1","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700017250"},{"key":"e_1_3_4_4_1","doi-asserted-by":"publisher","DOI":"10.1561\/2400000011"},{"key":"e_1_3_4_5_1","unstructured":"H. Hu and B. Yang Affine FR: An effective facial reduction algorithm for semidefinite relaxations of combinatorial problems (2024). Available at arXiv 2402.11796."},{"key":"e_1_3_4_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-022-01883-8"},{"key":"e_1_3_4_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-017-1136-5"},{"key":"e_1_3_4_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-019-01439-3"},{"issue":"3","key":"e_1_3_4_9_1","first-page":"241","article-title":"A structural geometrical analysis of weakly infeasible SDPs","volume":"59","author":"Louren\u00e7o B.F.","year":"2016","unstructured":"B.F. Louren\u00e7o, M. Muramatsu, and T. Tsuchiya, A structural geometrical analysis of weakly infeasible SDPs, J. Oper. Res. Soc. Jpn. 59(3) (2016), pp. 241\u2013257.","journal-title":"J. Oper. Res. Soc. Jpn."},{"key":"e_1_3_4_10_1","doi-asserted-by":"publisher","DOI":"10.1137\/15M1051634"},{"key":"e_1_3_4_11_1","doi-asserted-by":"publisher","DOI":"10.1080\/10556788.2020.1850720"},{"key":"e_1_3_4_12_1","doi-asserted-by":"crossref","unstructured":"G. Pataki The geometry of semidefinite programming in Handbook of Semidefinite Programming: Theory Algorithms and Applications H. Wolkowicz R. Saigal and L. Vandenberghe eds. Springer New York NY 2000.","DOI":"10.1007\/978-1-4615-4381-7_3"},{"key":"e_1_3_4_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-7621-4_28"},{"key":"e_1_3_4_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-022-09552-0"},{"key":"e_1_3_4_15_1","doi-asserted-by":"publisher","DOI":"10.1137\/21M1434945"},{"key":"e_1_3_4_16_1","doi-asserted-by":"publisher","DOI":"10.1137\/15M1049415"},{"key":"e_1_3_4_17_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-017-1169-9"},{"key":"e_1_3_4_18_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623495294955"},{"key":"e_1_3_4_19_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02614433"},{"key":"e_1_3_4_20_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623495288350"},{"key":"e_1_3_4_21_1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970524"},{"key":"e_1_3_4_22_1","volume-title":"Convex Analysis","author":"Rockafellar R.T.","year":"1997","unstructured":"R.T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, NJ, 1997."},{"key":"e_1_3_4_23_1","unstructured":"S. Sremac H. Woerdeman and H. Wolkowicz Complete facial reduction in one step for spectrahedra e-prints (2017). Available at arXiv 1710.07410."},{"key":"e_1_3_4_24_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623498338606"},{"key":"e_1_3_4_25_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-022-01891-8"},{"key":"e_1_3_4_26_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11590-011-0384-1"},{"key":"e_1_3_4_27_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-012-0219-y"},{"key":"e_1_3_4_28_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-4381-7"},{"key":"e_1_3_4_29_1","doi-asserted-by":"publisher","DOI":"10.1007\/s12532-019-00164-4"}],"container-title":["Optimization Methods and Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.tandfonline.com\/doi\/pdf\/10.1080\/10556788.2024.2409710","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T08:06:33Z","timestamp":1775549193000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.tandfonline.com\/doi\/full\/10.1080\/10556788.2024.2409710"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,2]]},"references-count":28,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2024,9,2]]}},"alternative-id":["10.1080\/10556788.2024.2409710"],"URL":"https:\/\/doi.org\/10.1080\/10556788.2024.2409710","relation":{},"ISSN":["1055-6788","1029-4937"],"issn-type":[{"value":"1055-6788","type":"print"},{"value":"1029-4937","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,9,2]]},"assertion":[{"value":"The publishing and review policy for this title is described in its Aims & Scope.","order":1,"name":"peerreview_statement","label":"Peer Review Statement"},{"value":"http:\/\/www.tandfonline.com\/action\/journalInformation?show=aimsScope&journalCode=goms20","URL":"http:\/\/www.tandfonline.com\/action\/journalInformation?show=aimsScope&journalCode=goms20","order":2,"name":"aims_and_scope_url","label":"Aim & Scope"},{"value":"2022-12-31","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-09-24","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-11-08","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}