{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:34:10Z","timestamp":1787340850923,"version":"build-2736575974"},"reference-count":21,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-11-LABX-0025-01"],"award-info":[{"award-number":["ANR-11-LABX-0025-01"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["666981"],"award-info":[{"award-number":["666981"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["306595"],"award-info":[{"award-number":["306595"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>We propose a moment relaxation for two problems, the separation and covering problems with semialgebraic sets generated by a polynomial of degree $d$. We show that (a) the optimal value of the relaxation finitely converges to the optimal value of the original problem, when the moment order $r$ increases, and (b) after performing some small perturbation of the original problem, convergence can be achieved with $r=d$. We further provide a practical iterative algorithm that is computationally tractable for large datasets and present encouraging computational results.<\/jats:p>","DOI":"10.1137\/18m1170108","type":"journal-article","created":{"date-parts":[[2018,11,13]],"date-time":"2018-11-13T14:25:33Z","timestamp":1542119133000},"page":"3127-3144","source":"Crossref","is-referenced-by-count":1,"title":["Optimal Data Fitting: A Moment Approach"],"prefix":"10.1137","volume":"28","author":[{"given":"Jean-Bernard","family":"Lasserre","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Victor","family":"Magron","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,11,13]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3216-0_8"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1147\/rd.266.0759"},{"key":"atypb3","first-page":"127","author":"Ben-Tal A.","year":"1979","journal-title":"New York"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1109\/TSMCA.2002.1021114"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-00-02472-7"},{"key":"atypb6","unstructured":"F. Glineur,\n                      Pattern separation via ellipsoids and conic programming\n                      , in M\u00e9moire de DEA, Facult\u00e9 Polytechnique de Mons, Belgium, 1998."},{"key":"atypb7","unstructured":"L. Gurobi,\n                      Gurobi Optimizer Reference Manual\n                      , 2018,http:\/\/www.gurobi.com."},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1109\/MCS.2004.1299534"},{"key":"atypb9","first-page":"187","author":"John F.","year":"1948","journal-title":"New York"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623400366802"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1137\/100806990"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-05-08133-5"},{"key":"atypb13","unstructured":"J. L\u00f6fberg,\n                      YALMIP : A toolbox for modeling and optimization in MATLAB\n                      , in Proceedings of the CACSD Conference, Taipei, Taiwan, 2004,http:\/\/users.isy.liu.se\/johanl\/yalmip."},{"key":"atypb14","unstructured":"A. Magnani, S. Lall, and S. Boyd,\n                      Tractable fitting with convex polynomials via sum-of-squares\n                      , in Proceedings of the 44th IEEE Conference on Decision and Control, Seville, Spain, December 2005."},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(65)90150-2"},{"key":"atypb16","doi-asserted-by":"crossref","unstructured":"J. F. Sturm,\n                      Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones\n                      , Optim. Methods Softw., 11 (1999), pp. 625-653.","DOI":"10.1080\/10556789908805766"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1040.0115"},{"key":"atypb18","doi-asserted-by":"crossref","unstructured":"M. Todd,\n                      Minimum-Volume Ellipsoids: Theory and Algorithms\n                      , MOS-SIAM Ser. Optim., SIAM, Philadelphia, 2016.","DOI":"10.1137\/1.9781611974386"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2007.02.013"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-002-0347-5"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479896303430"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/18M1170108","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:52:23Z","timestamp":1787338343000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/18M1170108"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":21,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/18M1170108"],"URL":"https:\/\/doi.org\/10.1137\/18m1170108","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}