{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T13:38:55Z","timestamp":1740145135800,"version":"3.37.3"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2022,7,15]],"date-time":"2022-07-15T00:00:00Z","timestamp":1657843200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,7,15]],"date-time":"2022-07-15T00:00:00Z","timestamp":1657843200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"crossref","award":["(B)19H023373"],"award-info":[{"award-number":["(B)19H023373"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Optim Lett"],"published-print":{"date-parts":[[2023,5]]},"DOI":"10.1007\/s11590-022-01908-3","type":"journal-article","created":{"date-parts":[[2022,7,15]],"date-time":"2022-07-15T11:05:32Z","timestamp":1657883132000},"page":"917-934","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Evaluating approximations of the semidefinite cone with trace normalized distance"],"prefix":"10.1007","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1073-9138","authenticated-orcid":false,"given":"Yuzhu","family":"Wang","sequence":"first","affiliation":[]},{"given":"Akiko","family":"Yoshise","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,7,15]]},"reference":[{"key":"1908_CR1","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1016\/j.disopt.2016.04.004","volume":"24","author":"AA Ahmadi","year":"2017","unstructured":"Ahmadi, A.A., Dash, S., Hall, G.: Optimization over structured subsets of positive semidefinite matrices via column generation. Discret. Optim. 24, 129\u2013151 (2017)","journal-title":"Discret. Optim."},{"key":"1908_CR2","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1137\/18M118935X","volume":"3","author":"AA Ahmadi","year":"2019","unstructured":"Ahmadi, A.A., Majumdar, A.: DSOS and SDSOS optimization: more tractable alternatives to sum of squares and semidefinite optimization. SIAM J. Appl. Algebra Geom. 3, 193\u2013230 (2019)","journal-title":"SIAM J. Appl. Algebra Geom."},{"key":"1908_CR3","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1007\/BF01898615","volume":"9","author":"H Bauer","year":"1958","unstructured":"Bauer, H.: Minimalstellen von Funktionen und Extremalpunkte. Archiv der Mathematik 9, 389\u2013393 (1958). https:\/\/doi.org\/10.1007\/BF01898615","journal-title":"Archiv der Mathematik"},{"issue":"1","key":"1908_CR4","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1016\/j.orl.2019.12.003","volume":"48","author":"D Bertsimas","year":"2020","unstructured":"Bertsimas, D., Cory-Wright, R.: On polyhedral and second-order cone decompositions of semidefinite optimization problems. Oper. Res. Lett. 48(1), 78\u201385 (2020)","journal-title":"Oper. Res. Lett."},{"key":"1908_CR5","doi-asserted-by":"publisher","first-page":"981","DOI":"10.1007\/s10107-020-01578-y","volume":"191","author":"G Blekherman","year":"2022","unstructured":"Blekherman, G., Dey, S.S., Molinaro, M., Sun, S.: Sparse PSD approximation of the PSD cone. Math. Program. 191, 981\u20131004 (2022)","journal-title":"Math. Program."},{"issue":"2","key":"1908_CR6","doi-asserted-by":"publisher","first-page":"470","DOI":"10.1137\/20M1387407","volume":"32","author":"G Blekherman","year":"2021","unstructured":"Blekherman, G., Dey, S.S., Shu, K., Sun, S.: Hyperbolic relaxation of $$k$$-locally positive semidefinite matrices. SIAM J. Optim. 32(2), 470\u2013490 (2021)","journal-title":"SIAM J. Optim."},{"key":"1908_CR7","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1016\/j.laa.2005.03.029","volume":"405","author":"EG Boman","year":"2005","unstructured":"Boman, E.G., Chen, D., Parekh, O., Toledo, S.: On factor width and symmetric H-matrices. Linear Algebra Appl. 405, 239\u2013248 (2005)","journal-title":"Linear Algebra Appl."},{"issue":"4","key":"1908_CR8","doi-asserted-by":"publisher","first-page":"1479","DOI":"10.1287\/moor.2020.1077","volume":"46","author":"H Fawzi","year":"2021","unstructured":"Fawzi, H.: On polyhedral approximations of the positive semidefinite cone. Math. Oper. Res. 46(4), 1479\u20131486 (2021)","journal-title":"Math. Oper. Res."},{"key":"1908_CR9","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1007\/s10107-005-0667-3","volume":"106","author":"RM Freund","year":"2006","unstructured":"Freund, R.M.: On the behavior of the homogeneous self-dual model for conic convex optimization. Math. Prog. 106, 527\u2013545 (2006)","journal-title":"Math. Prog."},{"key":"1908_CR10","doi-asserted-by":"publisher","first-page":"1115","DOI":"10.1145\/227683.227684","volume":"42","author":"MX Goemans","year":"1995","unstructured":"Goemans, M.X., Williamson, D.P.: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. ACM 42, 1115\u20131145 (1995)","journal-title":"J. ACM"},{"key":"1908_CR11","volume-title":"Matrix Anal.","author":"RA Horn","year":"1990","unstructured":"Horn, R.A., Johnson, C.R.: Matrix Anal. Cambridge University Press, Cambridge (1990)"},{"key":"1908_CR12","doi-asserted-by":"crossref","unstructured":"Kozhasov, K.: On eigenvalues of symmetric matrices with PSD principal submatrices. arXiv preprint arXiv:2103.15811 (2021)","DOI":"10.2139\/ssrn.4290288"},{"key":"1908_CR13","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1007\/3-540-45535-3_23","volume-title":"Integer programming and combinatorial optimization","author":"JB Lasserre","year":"2001","unstructured":"Lasserre, J.B.: An explicit exact SDP relaxation for nonlinear 0\u20131 programs. In: Aardal, K., Gerards, B. (eds.) Integer programming and combinatorial optimization, pp. 293\u2013303. Springer, Heidelberg (2001)"},{"key":"1908_CR14","unstructured":"MOSEK ApS: The MOSEK optimization toolbox for MATLAB manual. Version 8.1.http:\/\/docs.mosek.com\/8.1\/toolbox\/index.html (2017). Accessed 12 Mar 2021"},{"key":"1908_CR15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10107-017-1169-9","volume":"171","author":"F Permenter","year":"2018","unstructured":"Permenter, F., Parrilo, P.: Partial facial reduction: simplified, equivalent SDPs via approximations of the PSD cone. Math. Program. 171, 1\u201354 (2018)","journal-title":"Math. Program."},{"key":"1908_CR16","volume-title":"Combinatorial optimization: polyhedra and efficiency","author":"A Schrijver","year":"2003","unstructured":"Schrijver, A.: Combinatorial optimization: polyhedra and efficiency, vol. 24. Springer, Berlin (2003)"},{"key":"1908_CR17","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1017\/S0962492901000071","volume":"10","author":"MJ Todd","year":"2001","unstructured":"Todd, M.J.: Semidefinite optimization. Acta Numer. 10, 515\u2013560 (2001)","journal-title":"Acta Numer."},{"key":"1908_CR18","doi-asserted-by":"publisher","first-page":"893","DOI":"10.1007\/s10589-020-00255-2","volume":"78","author":"Y Wang","year":"2021","unstructured":"Wang, Y., Tanaka, A., Yoshise, A.: Polyhedral approximations of the semidefinite cone and their application. Comput. Optim. Appl. 78, 893\u2013913 (2021). https:\/\/doi.org\/10.1007\/s10589-020-00255-2","journal-title":"Comput. Optim. Appl."},{"key":"1908_CR19","volume-title":"Handbook of semidefinite programming: theory, algorithms, and applications","author":"H Wolkowicz","year":"2012","unstructured":"Wolkowicz, H., Saigal, R., Vandenberghe, L.: Handbook of semidefinite programming: theory, algorithms, and applications, vol. 27. Springer, Berlin (2012)"}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-022-01908-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11590-022-01908-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-022-01908-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,12]],"date-time":"2023-04-12T13:18:28Z","timestamp":1681305508000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11590-022-01908-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,15]]},"references-count":19,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023,5]]}},"alternative-id":["1908"],"URL":"https:\/\/doi.org\/10.1007\/s11590-022-01908-3","relation":{},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"type":"print","value":"1862-4472"},{"type":"electronic","value":"1862-4480"}],"subject":[],"published":{"date-parts":[[2022,7,15]]},"assertion":[{"value":"28 May 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 June 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 July 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}