{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:03:32Z","timestamp":1787321012198,"version":"build-2736575974"},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2005,12,1]],"date-time":"2005-12-01T00:00:00Z","timestamp":1133395200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2005,12]]},"DOI":"10.1007\/s10898-005-2099-2","type":"journal-article","created":{"date-parts":[[2005,11,23]],"date-time":"2005-11-23T12:43:07Z","timestamp":1132749787000},"page":"511-525","source":"Crossref","is-referenced-by-count":10,"title":["Minimum Ellipsoid Bounds for Solutions of Polynomial Systems via Sum of Squares"],"prefix":"10.1007","volume":"33","author":[{"given":"Jiawang","family":"Nie","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"James W.","family":"Demmel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"key":"2099_CR1","doi-asserted-by":"crossref","unstructured":"Bochnak J., Coste M., Roy MF. (1998). Real Algebraic Geometry, Springer.","DOI":"10.1007\/978-3-662-03718-8"},{"issue":"2","key":"2099_CR2","first-page":"103","volume":"58","author":"M.D. Choi","year":"1995","journal-title":"Proceedings of Symposia in Pure Mathematics."},{"key":"2099_CR3","unstructured":"Calafiore G. and El Ghaoui L. (1999).Confidence ellipsoids for uncertain linear equations with structure. Proc. Conf. Decision and Control. December."},{"key":"2099_CR4","unstructured":"Calafiore, G. and El Ghaoui, L.Ellipsoid bounds for uncertain linear equations and dynamical systems, to appear in Automatica. http:\/\/robotics.eecs.berkeley.edu\/\u223celghaoui."},{"issue":"2","key":"2099_CR5","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/PL00004868","volume":"237","author":"T. Jacobi","year":"2001","journal-title":"Mathematische Zeitschrift."},{"issue":"3","key":"2099_CR6","doi-asserted-by":"crossref","first-page":"796","DOI":"10.1137\/S1052623400366802","volume":"11","author":"Lasserre","year":"2001","journal-title":"SIAM Journal of Optimization."},{"key":"2099_CR7","doi-asserted-by":"crossref","unstructured":"Nesterov Yu. (2000). Squared functional systems and optimization problems. In: Frenk, H. et al. (eds.).High Performance Optimization, Kluwer Academic Publishers, pp. 405\u2013440.","DOI":"10.1007\/978-1-4757-3216-0_17"},{"key":"2099_CR8","unstructured":"Parrilo, Pablo A. (2000). Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization. Ph.D Thesis, Californial Institute of Technology."},{"key":"2099_CR9","unstructured":"Prajna, S., Papachristodoulou, A. and Parrilo, Pablo A. SOSTOOLS User\u2019s Guide.http:\/\/control.ee.ethz.ch\/\u223cparrilo\/SOSTOOLS\/."},{"key":"2099_CR10","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1007\/s10107-003-0387-5","volume":"2","author":"Parrilo","year":"2003","journal-title":"Mathematical Program no.Ser. B. 96"},{"key":"2099_CR11","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1512\/iumj.1993.42.42045","volume":"42","author":"M. Putinar","year":"1993","journal-title":"Indiana University, Mathematics Journal."},{"key":"2099_CR12","unstructured":"Reznick B. (2000). Some concrete aspects of Hilbert\u2019s 17th problem. In: Contemporary Mathematics Vol. 253, American Mathematical Society. pp. 251\u2013272."},{"key":"2099_CR13","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/BF01446568","volume":"289","author":"K. Schm\u00fcdgen","year":"1991","journal-title":"Mathematische Annalen."},{"key":"2099_CR14","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1016\/j.jco.2004.01.005","volume":"20","author":"M. Schweighofer","year":"2004","journal-title":"Journal of Complexity."},{"key":"2099_CR15","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/BF01362149","volume":"207","author":"G. Stengle","year":"1974","journal-title":"Mathematische Annalen."},{"key":"2099_CR16","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1006\/jcom.1996.0011","volume":"12","author":"G. Stengle","year":"1996","journal-title":"Journal of Complexity."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-005-2099-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-005-2099-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-005-2099-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T08:12:03Z","timestamp":1559290323000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-005-2099-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,12]]},"references-count":16,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2005,12]]}},"alternative-id":["2099"],"URL":"https:\/\/doi.org\/10.1007\/s10898-005-2099-2","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,12]]}}}