{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,16]],"date-time":"2024-09-16T19:14:15Z","timestamp":1726514055589},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2014,10,14]],"date-time":"2014-10-14T00:00:00Z","timestamp":1413244800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Optim Lett"],"published-print":{"date-parts":[[2015,8]]},"DOI":"10.1007\/s11590-014-0812-0","type":"journal-article","created":{"date-parts":[[2014,10,13]],"date-time":"2014-10-13T15:32:46Z","timestamp":1413214366000},"page":"1063-1073","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Strong duality for generalized trust region subproblem: S-lemma with interval bounds"],"prefix":"10.1007","volume":"9","author":[{"given":"Shu","family":"Wang","sequence":"first","affiliation":[]},{"given":"Yong","family":"Xia","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,10,14]]},"reference":[{"key":"812_CR1","first-page":"51","volume":"72","author":"A Ben-Tal","year":"1996","unstructured":"Ben-Tal, A., Teboulle, M.: Hidden convexity in some nonconvex quadratically constrained quadratic programming. Math. Program. 72, 51\u201363 (1996)","journal-title":"Math. Program."},{"key":"812_CR2","doi-asserted-by":"crossref","unstructured":"Conn, A.R., Gould, N.I.M., Toint, Ph.L.: Trust-Region Methods. SIAM, Philadelphia (2000)","DOI":"10.1137\/1.9780898719857"},{"key":"812_CR3","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/s00186-006-0070-8","volume":"64","author":"K Derinkuyu","year":"2006","unstructured":"Derinkuyu, K., Pinar, M.\u00c7.: On the S-procedure and some variants. Math. Methods Oper. Res. 64, 55\u201377 (2006)","journal-title":"Math. Methods Oper. Res."},{"issue":"1","key":"812_CR4","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/0377-2217(95)00199-9","volume":"94","author":"OE Flippo","year":"1996","unstructured":"Flippo, O.E., Jansen, B.: Duality and sensitivity in nonconvex quadratic optimization over an ellipsoid. Eur. J. Oper. Res. 94(1), 167\u2013178 (1996)","journal-title":"Eur. J. Oper. Res."},{"issue":"1","key":"812_CR5","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1080\/10556780410001647186","volume":"19","author":"C Fortin","year":"2004","unstructured":"Fortin, C., Wolkowicz, H.: The trust region subproblem and semidefinite programming. Optim. Methods Softw. 19(1), 41\u201367 (2004)","journal-title":"Optim. Methods Softw."},{"key":"812_CR6","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1137\/0902016","volume":"2","author":"DM Gay","year":"1981","unstructured":"Gay, D.M.: Computing optimal locally constrained steps. SIAM J. Sci. Stat. Comput. 2, 186\u2013197 (1981)","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"812_CR7","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511810817","volume-title":"Matrix Analysis","author":"R Horn","year":"1985","unstructured":"Horn, R., Johnson, C.R.: Matrix Analysis. Cambridge University Press, Cambridge (1985)"},{"key":"812_CR8","unstructured":"Hsia, Y., Lin, G.X., Sheu, R.L.: A revisit to quadratic programming with one inequality quadratic constraint via matrix pencil. Pacific J. Optim. 10(3), 461\u2013481 (2014)"},{"key":"812_CR9","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1137\/0904038","volume":"4","author":"JJ Mor\u00e9","year":"1983","unstructured":"Mor\u00e9, J.J., Sorensen, D.C.: Computing a trust region step. SIAM J. Sci. Stat. Comput. 4, 553\u2013572 (1983)","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"812_CR10","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1080\/10556789308805542","volume":"2","author":"JJ Mor\u00e9","year":"1993","unstructured":"Mor\u00e9, J.J.: Generalizations of the trust region problem. Optim. Methods Softw. 2, 189\u2013209 (1993)","journal-title":"Optim. Methods Softw."},{"issue":"3","key":"812_CR11","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1137\/S003614450444614X","volume":"49","author":"I P\u00f3lik","year":"2007","unstructured":"P\u00f3lik, I., Terlaky, T.: A Survey of S-lemma. SIAM review. 49(3), 371\u2013418 (2007)","journal-title":"A Survey of S-lemma. SIAM review."},{"key":"812_CR12","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1023\/A:1021798932766","volume":"99","author":"BT Polyak","year":"1998","unstructured":"Polyak, B.T.: Convexity of quadratic transformations and its use in control and optimization. J. Optim. Theory Appl. 99, 553\u2013583 (1998)","journal-title":"J. Optim. Theory Appl."},{"issue":"2","key":"812_CR13","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/s10589-013-9635-7","volume":"58","author":"TK Pong","year":"2014","unstructured":"Pong, T.K., Wolkowicz, H.: Generalizations of the trust region subproblem. Comput. Optim. Appl. 58(2), 273\u2013322 (2014)","journal-title":"Comput. Optim. Appl."},{"issue":"2","key":"812_CR14","first-page":"273","volume":"77","author":"F Rendl","year":"1997","unstructured":"Rendl, F., Wolkowicz, H.: A semidefinite framework for trust region subproblems with applications to large scale minimization. Math. Program. 77(2), 273\u2013299 (1997)","journal-title":"Math. Program."},{"issue":"2","key":"812_CR15","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1137\/0805016","volume":"5","author":"R Stern","year":"1995","unstructured":"Stern, R., Wolkowicz, H.: Indefinite trust region subproblems and nonsymmetric eigenvalue perturbations. SIAM J. Optim. 5(2), 286\u2013313 (1995)","journal-title":"SIAM J. Optim."},{"key":"812_CR16","unstructured":"Xia, Y., Wang, S., Sheu, R.L.: S-lemma with Equality and its Applications. (2014). arXiv:1403.2816"},{"key":"812_CR17","first-page":"62","volume":"1","author":"VA Yakubovich","year":"1971","unstructured":"Yakubovich, V.A.: S-procedure in nonlinear control theory. Vestn. Leningrad Univ. 1, 62\u201377 (1971). (in Russian)","journal-title":"Vestn. Leningrad Univ."},{"key":"812_CR18","first-page":"73","volume":"4","author":"VA Yakubovich","year":"1977","unstructured":"Yakubovich, V.A.: S-procedure in nonlinear control theory. Vestn. Leningrad Univ. 4, 73\u201393 (1977). (English translation)","journal-title":"Vestn. Leningrad Univ."},{"key":"812_CR19","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1137\/S105262340139001X","volume":"14","author":"Y Ye","year":"2003","unstructured":"Ye, Y., Zhang, S.: New results on quadratic minimization. SIAM J. Optim. 14, 245\u2013267 (2003)","journal-title":"SIAM J. Optim."}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-014-0812-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11590-014-0812-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-014-0812-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T17:11:40Z","timestamp":1559409100000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11590-014-0812-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,10,14]]},"references-count":19,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2015,8]]}},"alternative-id":["812"],"URL":"https:\/\/doi.org\/10.1007\/s11590-014-0812-0","relation":{},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"value":"1862-4472","type":"print"},{"value":"1862-4480","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,10,14]]}}}