{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T06:47:38Z","timestamp":1776754058881,"version":"3.51.2"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2019,5,15]],"date-time":"2019-05-15T00:00:00Z","timestamp":1557878400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,5,15]],"date-time":"2019-05-15T00:00:00Z","timestamp":1557878400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100006188","name":"Einstein Stiftung Berlin","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100006188","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2020,7]]},"DOI":"10.1007\/s10107-019-01399-8","type":"journal-article","created":{"date-parts":[[2019,5,15]],"date-time":"2019-05-15T22:30:59Z","timestamp":1557959459000},"page":"399-428","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["The geometry of SDP-exactness in quadratic optimization"],"prefix":"10.1007","volume":"182","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0222-3761","authenticated-orcid":false,"given":"Diego","family":"Cifuentes","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Corey","family":"Harris","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bernd","family":"Sturmfels","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,5,15]]},"reference":[{"key":"1399_CR1","doi-asserted-by":"crossref","unstructured":"Blekherman, G., Parrilo, P.A., Thomas, R.R., (Eds.) Semidefinite Optimization and Convex Algebraic Geometry. MOS-SIAM Series on Optimization, vol 13, Philadelphia, PA: SIAM (2013)","DOI":"10.1145\/2465506.2466575"},{"key":"1399_CR2","doi-asserted-by":"publisher","first-page":"893","DOI":"10.1090\/jams\/847","volume":"29","author":"G Blekherman","year":"2016","unstructured":"Blekherman, G., Smith, G., Velasco, M.: Sums of squares and varieties of minimal degree. J. Am. Math. Soc. 29, 893\u2013913 (2016)","journal-title":"J. Am. Math. Soc."},{"key":"1399_CR3","unstructured":"Cifuentes, D., Agarwal, S., Parrilo, P., Thomas, R.: On the local stability of semidefinite relaxations. arXiv:1710.04287"},{"key":"1399_CR4","doi-asserted-by":"crossref","unstructured":"Cifuentes, D., Ranestad, K., Sturmfels, B., Weinstein, M.: Voronoi cells of varieties. In: International Conference on Effective Methods in Algebraic Geometry (MEGA). To be presented in June (2019)","DOI":"10.1016\/j.jsc.2020.07.009"},{"key":"1399_CR5","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1023\/A:1004927626862","volume":"67","author":"W Degen","year":"1997","unstructured":"Degen, W.: The cut locus of an ellipsoid. Geom. Dedic. 67, 197\u2013198 (1997)","journal-title":"Geom. Dedic."},{"key":"1399_CR6","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1007\/s10208-014-9240-x","volume":"16","author":"J Draisma","year":"2016","unstructured":"Draisma, J., Horobe\u0163, E., Ottaviani, G., Sturmfels, B., Thomas, R.: The Euclidean distance degree of an algebraic variety. Found. Comput. Math. 16, 99\u2013149 (2016)","journal-title":"Found. Comput. Math."},{"key":"1399_CR7","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1112\/blms\/bdn114","volume":"41","author":"H-C Graf von Bothmer","year":"2009","unstructured":"Graf von Bothmer, H.-C., Ranstad, K.: A general formula for the algebraic degree in semidefinite programming. Bull. Lond. Math. Soc. 41, 193\u2013197 (2009)","journal-title":"Bull. Lond. Math. Soc."},{"issue":"6","key":"1399_CR8","doi-asserted-by":"publisher","first-page":"1115","DOI":"10.1145\/227683.227684","volume":"42","author":"M Goemans","year":"1995","unstructured":"Goemans, M., Williamson, D.: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. ACM 42(6), 1115\u20131145 (1995)","journal-title":"J. ACM"},{"key":"1399_CR9","doi-asserted-by":"publisher","first-page":"2097","DOI":"10.1137\/090746525","volume":"20","author":"J Gouveia","year":"2010","unstructured":"Gouveia, J., Parrilo, P., Thomas, R.: Theta bodies for polynomial ideals. SIAM J. Optim. 20, 2097\u20132118 (2010)","journal-title":"SIAM J. Optim."},{"key":"1399_CR10","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/0040-9383(84)90026-0","volume":"23","author":"J Harris","year":"1984","unstructured":"Harris, J., Tu, L.: On symmetric and skew-symmetric determinantal varieties. Topology 23, 71\u201384 (1984)","journal-title":"Topology"},{"key":"1399_CR11","unstructured":"Helmberg, C.: Semidefinite programming for combinatorial optimization, ZIB-Report ZR 00-34, Konrad-Zuse-Zentrum f\u00fcr Informationstechnik Berlin (2000)"},{"key":"1399_CR12","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1016\/0024-3795(95)00271-R","volume":"223","author":"M Laurent","year":"1995","unstructured":"Laurent, M., Poljak, S.: On a positive semidefinite relaxation of the cut polytope. Linear Algebra Appl. 223, 439\u2013461 (1995)","journal-title":"Linear Algebra Appl."},{"issue":"3","key":"1399_CR13","doi-asserted-by":"publisher","first-page":"796","DOI":"10.1137\/S1052623400366802","volume":"11","author":"J-B Lasserre","year":"2001","unstructured":"Lasserre, J.-B.: Global optimization with polynomials and the problem of moments. SIAM J. Optim. 11(3), 796\u2013817 (2001)","journal-title":"SIAM J. Optim."},{"key":"1399_CR14","volume-title":"Moments, Positive Polynomials and Their Applications","author":"J-B Lasserre","year":"2010","unstructured":"Lasserre, J.-B.: Moments, Positive Polynomials and Their Applications. World Scientific, Singapore (2010)"},{"key":"1399_CR15","volume-title":"Algebraic Geometry I: Complex Projective Varieties","author":"D Mumford","year":"1976","unstructured":"Mumford, D.: Algebraic Geometry I: Complex Projective Varieties. Springer, Berlin (1976)"},{"key":"1399_CR16","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1137\/080716670","volume":"20","author":"J Nie","year":"2009","unstructured":"Nie, J., Ranestad, K.: Algebraic degree of polynomial optimization. SIAM J. Optim. 20, 485\u2013502 (2009)","journal-title":"SIAM J. Optim."},{"key":"1399_CR17","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1007\/s10107-008-0253-6","volume":"122","author":"J Nie","year":"2010","unstructured":"Nie, J., Ranestad, K., Sturmfels, B.: The algebraic degree of semidefinite programming. Math. Program. 122, 379\u2013405 (2010)","journal-title":"Math. Program."},{"issue":"1","key":"1399_CR18","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1137\/17M1118981","volume":"2","author":"C Scheiderer","year":"2018","unstructured":"Scheiderer, C.: Spectrahedral shadows. SIAM J. Appl. Algebra Geom. 2(1), 26\u201344 (2018)","journal-title":"SIAM J. Appl. Algebra Geom."},{"key":"1399_CR19","first-page":"1","volume":"25","author":"N-Z Shor","year":"1987","unstructured":"Shor, N.-Z.: Quadratic optimization problems. Sov. J. Comput. Syst. Sci. 25, 1\u201311 (1987)","journal-title":"Sov. J. Comput. Syst. Sci."},{"key":"1399_CR20","doi-asserted-by":"publisher","first-page":"1209","DOI":"10.1137\/140978478","volume":"25","author":"R Sinn","year":"2015","unstructured":"Sinn, R., Sturmfels, B.: Generic spectrahedral shadows. SIAM J. Optim. 25, 1209\u20131220 (2015)","journal-title":"SIAM J. Optim."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-019-01399-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-019-01399-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-019-01399-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,12]],"date-time":"2020-12-12T23:49:19Z","timestamp":1607816959000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-019-01399-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,15]]},"references-count":20,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2020,7]]}},"alternative-id":["1399"],"URL":"https:\/\/doi.org\/10.1007\/s10107-019-01399-8","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,5,15]]},"assertion":[{"value":"5 April 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 April 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 May 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}