{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,26]],"date-time":"2026-09-26T01:17:39Z","timestamp":1790385459051,"version":"4.1.0"},"reference-count":19,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004489","name":"Mitacs","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004489","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>The projection onto the intersection of sets generally does not allow for a closed form even when the individual projection operators have explicit descriptions. In this work, we systematically analyze the projection onto the intersection of a cone with either a ball or a sphere. Several cases are provided where the projector is available in closed form. Various examples based on finitely generated cones, the Lorentz cone, and the cone of positive semidefinite matrices are presented. The usefulness of our formulae is illustrated by numerical experiments for determining copositivity of real symmetric matrices.<\/jats:p>","DOI":"10.1137\/17m1141849","type":"journal-article","created":{"date-parts":[[2018,8,2]],"date-time":"2018-08-02T13:02:02Z","timestamp":1533214922000},"page":"2158-2188","source":"Crossref","is-referenced-by-count":32,"title":["Projecting onto the Intersection of a Cone and a Sphere"],"prefix":"10.1137","volume":"28","author":[{"given":"Heinz H.","family":"Bauschke","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Minh N.","family":"Bui","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xianfu","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,8,2]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(69)90200-5"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-011-0484-9"},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"H. H. Bauschke and P. L. Combettes,\n                      Convex Analysis and Monotone Operator Theory in Hilbert Spaces\n                      , CMS Books Math., 2nd ed., Springer, New York, 2017.","DOI":"10.1007\/978-3-319-48311-5"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/080716542"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-013-0701-9"},{"key":"atypb6","unstructured":"M. Du\u0308r,\n                      Copositive programming: A survey\n                      , in Recent Advances in Optimization and its Applications in Engineering, M. Diehl, F. Glineur, E. Jarlebring, and W. Michiels, eds., Springer, Berlin, 2010."},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-012-9914-3"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(83)90095-2"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100036951"},{"key":"atypb10","unstructured":"Y. Haugazeau,\n                      Sur les ine\u0301quations variationnelles et la minimisation de fonctionnelles convexes\n                      , The\u0300se, Universite\u0301 de Paris, Paris, 1968."},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1137\/090750391"},{"key":"atypb12","doi-asserted-by":"crossref","unstructured":"K. Lange,\n                      MM Optimization Algorithms\n                      , Other Titles Appl. Math. 147, SIAM, Philadelphia, PA, 2016.","DOI":"10.1137\/1.9781611974409"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1070.0291"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-015-0963-5"},{"key":"atypb15","first-page":"238","volume":"225","author":"Moreau J.-J.","year":"1962","journal-title":"C. R. Acad. Sci. Se\u0301r. A."},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(93)90116-6"},{"key":"atypb17","unstructured":"R. T. Rockafellar,\n                      Convex Analysis\n                      , Princeton University Press, Princeton, NJ, 1970."},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100051070"},{"key":"atypb19","first-page":"91","author":"Yu Y.-L.","year":"2013","journal-title":"NY"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/17M1141849","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:18:57Z","timestamp":1787339937000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/17M1141849"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":19,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/17M1141849"],"URL":"https:\/\/doi.org\/10.1137\/17m1141849","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}