{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,29]],"date-time":"2026-03-29T06:56:48Z","timestamp":1774767408187,"version":"3.50.1"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2018,12,12]],"date-time":"2018-12-12T00:00:00Z","timestamp":1544572800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11801557"],"award-info":[{"award-number":["11801557"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11701177"],"award-info":[{"award-number":["11701177"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11771243"],"award-info":[{"award-number":["11771243"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11501543"],"award-info":[{"award-number":["11501543"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11701512"],"award-info":[{"award-number":["11701512"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"crossref","award":["2017MS058"],"award-info":[{"award-number":["2017MS058"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"crossref","award":["800015LF"],"award-info":[{"award-number":["800015LF"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"crossref","award":["2018ZD14"],"award-info":[{"award-number":["2018ZD14"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Zhejiang Provincial Natural Science Foundation of China","award":["LQ16A010010"],"award-info":[{"award-number":["LQ16A010010"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2019,2]]},"DOI":"10.1007\/s10898-018-0726-y","type":"journal-article","created":{"date-parts":[[2018,12,12]],"date-time":"2018-12-12T05:16:48Z","timestamp":1544591808000},"page":"371-388","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["A sensitive-eigenvector based global algorithm for quadratically constrained quadratic programming"],"prefix":"10.1007","volume":"73","author":[{"given":"Cheng","family":"Lu","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0563-5841","authenticated-orcid":false,"given":"Zhibin","family":"Deng","sequence":"additional","affiliation":[]},{"given":"Jing","family":"Zhou","sequence":"additional","affiliation":[]},{"given":"Xiaoling","family":"Guo","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,12,12]]},"reference":[{"key":"726_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s12532-008-0001-1","volume":"1","author":"T Achterberg","year":"2009","unstructured":"Achterberg, T.: SCIP: solving constraint integer programs. Math. Program. Comput. 1, 1\u201341 (2009)","journal-title":"Math. Program. Comput."},{"key":"726_CR2","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1023\/A:1008240227198","volume":"13","author":"LTH An","year":"1998","unstructured":"An, L.T.H., Tao, P.D.: A branch and bound method via D.C. optimization algorithms and ellipsoidal technique for box constrained nonconvex quadratic problems. J. Glob. Optim. 13, 171\u2013206 (1998)","journal-title":"J. Glob. Optim."},{"key":"726_CR3","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1080\/10556780902883184","volume":"24","author":"X Bao","year":"2009","unstructured":"Bao, X., Sahinidis, N.V.: Polyhedral relaxations for nonconvex, quadratically constrained quadratic programs. Optim. Method Softw. 24, 485\u2013504 (2009)","journal-title":"Optim. Method Softw."},{"key":"726_CR4","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/s10107-011-0462-2","volume":"129","author":"X Bao","year":"2011","unstructured":"Bao, X., Sahinidis, N.V., Tawarmalani, M.: Semidefinite relaxations for quadratically constrained quadratic programs: a review and comparisons. Math. Program. 129, 129\u2013157 (2011)","journal-title":"Math. Program."},{"key":"726_CR5","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":"726_CR6","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1007\/s10107-012-0534-y","volume":"141","author":"C Buchheim","year":"2013","unstructured":"Buchheim, C., Wiegele, A.: Semidefinite relaxations for non-convex quadratic mixed-integer programming. Math. Program. 141, 435\u2013452 (2013)","journal-title":"Math. Program."},{"key":"726_CR7","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1007\/s10107-006-0080-6","volume":"113","author":"S Burer","year":"2008","unstructured":"Burer, S., Vandenbussche, D.: A finite branch-and-bound algorithm for nonconvex quadratic programming via semidefinite relaxations. Math. Program. 113, 259\u2013282 (2008)","journal-title":"Math. Program."},{"key":"726_CR8","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1007\/s10107-015-0888-z","volume":"151","author":"S Burer","year":"2015","unstructured":"Burer, S.: A gentle, geometric introduction to copositive optimization. Math. Program. 151, 89\u2013116 (2015)","journal-title":"Math. Program."},{"key":"726_CR9","doi-asserted-by":"publisher","first-page":"316","DOI":"10.1007\/s10898-004-6095-8","volume":"33","author":"R Cambini","year":"2005","unstructured":"Cambini, R., Sodini, C.: Decomposition methods for solving nonconvex quadratic programs via branch and bound. J. Glob. Optim. 33, 316\u2013336 (2005)","journal-title":"J. Glob. Optim."},{"key":"726_CR10","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/s12532-011-0033-9","volume":"4","author":"J Chen","year":"2012","unstructured":"Chen, J., Burer, S.: Globally solving nonconvex quadratic programming problems via completely positive programming. Math. Program. Comput. 4, 33\u201352 (2012)","journal-title":"Math. Program. Comput."},{"key":"726_CR11","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1137\/070679041","volume":"19","author":"S He","year":"2008","unstructured":"He, S., Luo, Z.-Q., Nie, J., Zhang, S.: Semidefinite relaxation bounds for indefinite homogeneous quadratic optimization. SIAM J. Optim. 19, 503\u2013523 (2008)","journal-title":"SIAM J. Optim."},{"key":"726_CR12","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1080\/10556780108805819","volume":"15","author":"S Kim","year":"2001","unstructured":"Kim, S., Kojima, M.: Second order cone programming relaxation of nonconvex quadratic optimization problems. Optim. Method Softw. 15, 201\u2013224 (2001)","journal-title":"Optim. Method Softw."},{"key":"726_CR13","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1007\/978-1-4613-0279-7_6","volume-title":"Proceedings of Advances in Convex Analysis and Global Optimization","author":"C Lemarechal","year":"2001","unstructured":"Lemarechal, C., Oustry, F.: SDP relaxations in combinatorial optimization from a Lagrangian point of view. In: Hadjisavvas, N., Pardalos, P. (eds.) Proceedings of Advances in Convex Analysis and Global Optimization, pp. 119\u2013134. Kluwer, Amsterdam (2001)"},{"key":"726_CR14","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1007\/s10107-005-0582-7","volume":"103","author":"J Linderoth","year":"2005","unstructured":"Linderoth, J.: A simplicial branch-and-bound algorithm for solving quadratically constrained quadratic programs. Math. Program. 103, 251\u2013282 (2005)","journal-title":"Math. Program."},{"key":"726_CR15","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1016\/S0024-3795(98)10032-0","volume":"284","author":"MS Lobo","year":"1998","unstructured":"Lobo, M.S., Vandenberghe, L., Boyd, S., Lebret, H.: Applications of second-order cone programming. Linear Algebra Appl. 284, 193\u2013228 (1998)","journal-title":"Linear Algebra Appl."},{"key":"726_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1137\/050642691","volume":"18","author":"Z-Q Luo","year":"2007","unstructured":"Luo, Z.-Q., Sidiropoulos, N.D., Tseng, P., Zhang, S.: Approximation bounds for quadratic optimization with homogeneous quadratic constraints. SIAM J. Optim. 18, 1\u201328 (2007)","journal-title":"SIAM J. Optim."},{"key":"726_CR17","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1109\/MSP.2010.936019","volume":"27","author":"Z-Q Luo","year":"2010","unstructured":"Luo, Z.-Q., Ma, W.-K., So, A.M.-C., Ye, Y., Zhang, S.: Semidefinite relaxation of quadratic optimization problems: from its practical deployments and scope of applicability to key theoretical results. IEEE Signal Process. Mag. 27, 20\u201334 (2010)","journal-title":"IEEE Signal Process. Mag."},{"key":"726_CR18","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1007\/s10898-016-0436-2","volume":"67","author":"C Lu","year":"2017","unstructured":"Lu, C., Deng, Z., Jin, Q.: An eigenvalue decomposition based branch-and-bound algorithm for nonconvex quadratic programming problems with convex quadratic constraints. J. Global Optim. 67, 475\u2013493 (2017)","journal-title":"J. Global Optim."},{"key":"726_CR19","doi-asserted-by":"publisher","first-page":"2682","DOI":"10.1109\/TWC.2008.070104","volume":"7","author":"E Matskani","year":"2008","unstructured":"Matskani, E., Sidiropoulos, N.D., Luo, Z.-Q., Tassiulas, L.: Convex approximation techniques for joint multiuser downlink beamforming and admission control. IEEE Trans. Wireless Commun. 7, 2682\u20132693 (2008)","journal-title":"IEEE Trans. Wireless Commun."},{"key":"726_CR20","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s10898-012-9874-7","volume":"57","author":"R Misener","year":"2013","unstructured":"Misener, R., Floudas, C.A.: GloMIQO: global mixed-integer quadratic optimizer. J. Global Optim. 57, 3\u201350 (2013)","journal-title":"J. Global Optim."},{"key":"726_CR21","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1007\/s10898-014-0166-2","volume":"59","author":"R Misener","year":"2014","unstructured":"Misener, R., Floudas, C.A.: ANTIGONE: algorithms for continuous\/integer global optimization of nonlinear equations. J. Global Optim. 59, 503\u2013526 (2014)","journal-title":"J. Global Optim."},{"key":"726_CR22","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1080\/10556788.2012.749876","volume":"29","author":"JE Mitchell","year":"2014","unstructured":"Mitchell, J.E., Pang, J.S., Yu, B.: Convex quadratic relaxations of nonconvex quadratically constrained quadratic programs. Optim. Method Softw. 29, 120\u2013136 (2014)","journal-title":"Optim. Method Softw."},{"key":"726_CR23","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1007\/BF02247879","volume":"45","author":"PM Pardalos","year":"1990","unstructured":"Pardalos, P.M., Rodgers, G.P.: Computational aspects of a branch and bound algorithm for quadratic zero-one programming. Computing 45, 131\u2013144 (1990)","journal-title":"Computing"},{"key":"726_CR24","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1007\/BF00120662","volume":"1","author":"PM Pardalos","year":"1991","unstructured":"Pardalos, P.M., Vavasis, S.A.: Quadratic programming with one negative eigenvalue is NP-hard. J. Global Optim. 1, 15\u201322 (1991)","journal-title":"J. Global Optim."},{"key":"726_CR25","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, 273\u2013299 (1997)","journal-title":"Math. Program."},{"key":"726_CR26","doi-asserted-by":"crossref","unstructured":"Sahinidis, N.V.: BARON: A general purpose global optimization software package. J. Global Optim. 8, 201\u2013205 (1996)","DOI":"10.1007\/BF00138693"},{"key":"726_CR27","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1007\/s10107-010-0340-3","volume":"130","author":"A Saxena","year":"2010","unstructured":"Saxena, A., Bonami, P., Lee, J.: Convex relaxations of non-convex mixed integer quadratically constrained programs: projected formulations. Math. Program. 130, 359\u2013413 (2010)","journal-title":"Math. Program."},{"key":"726_CR28","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1007\/s10107-010-0371-9","volume":"124","author":"A Saxena","year":"2010","unstructured":"Saxena, A., Bonami, P., Lee, J.: Convex relaxations of non-convex mixed integer quadratically constrained programs: extended formulations. Math. Program. 124, 383\u2013411 (2010)","journal-title":"Math. Program."},{"key":"726_CR29","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1137\/0403036","volume":"3","author":"HD Sherali","year":"1990","unstructured":"Sherali, H.D., Adams, W.P.: A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems. SIAM J. Discrete Math. 3, 411\u2013430 (1990)","journal-title":"SIAM J. Discrete Math."},{"key":"726_CR30","unstructured":"Sherali, H.D., Liberti, L.: Reformulation-Linearization methods for global optimization. Technical report"},{"key":"726_CR31","doi-asserted-by":"publisher","first-page":"2239","DOI":"10.1109\/TSP.2006.872578","volume":"54","author":"ND Sidiropoulos","year":"2006","unstructured":"Sidiropoulos, N.D., Davidson, T.N., Luo, Z.-Q.: Transmit beamforming for physical layer multicasting. IEEE Trans. Signal Process. 54, 2239\u20132251 (2006)","journal-title":"IEEE Trans. Signal Process."},{"key":"726_CR32","doi-asserted-by":"publisher","first-page":"1746","DOI":"10.1137\/130915261","volume":"24","author":"S Sojoudi","year":"2014","unstructured":"Sojoudi, S., Lavaei, J.: Exactness of semidefinite relaxations for nonlinear optimization problems with underlying graph structure. SIAM J. Optim. 24, 1746\u20131778 (2014)","journal-title":"SIAM J. Optim."},{"key":"726_CR33","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1287\/moor.28.2.246.14485","volume":"28","author":"JF Sturm","year":"2003","unstructured":"Sturm, J.F., Zhang, S.: On cones of nonnegative quadratic functions. Math. Oper. Res. 28, 246\u2013267 (2003)","journal-title":"Math. Oper. Res."},{"key":"726_CR34","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1080\/10556789908805766","volume":"11","author":"JF Sturm","year":"1999","unstructured":"Sturm, J.F.: Using SeDuMi 1.02, a Matlab toolbox for optimization over symmetric cones. Optim. Method Softw. 11, 625\u2013653 (1999)","journal-title":"Optim. Method Softw."},{"key":"726_CR35","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1007\/s10107-005-0581-8","volume":"103","author":"M Tawarmalani","year":"2005","unstructured":"Tawarmalani, M., Sahinidis, N.V.: A polyhedral branch-and-cut approach to global optimization. Math. Program. 103, 225\u2013249 (2005)","journal-title":"Math. Program."},{"key":"726_CR36","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1007\/s10107-004-0550-7","volume":"102","author":"D Vandenbussche","year":"2005","unstructured":"Vandenbussche, D., Nemhauser, G.L.: A branch-and-cut algorithm for nonconvex quadratic programs with box constraints. Math. Program. 102, 559\u2013575 (2005)","journal-title":"Math. Program."},{"key":"726_CR37","doi-asserted-by":"crossref","unstructured":"W\u00e4chter, A., Biegler, L.T.: On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Math. Program. 106, 25\u201357 (2006)","DOI":"10.1007\/s10107-004-0559-y"},{"key":"726_CR38","doi-asserted-by":"publisher","first-page":"1565","DOI":"10.1137\/15M1047167","volume":"26","author":"S Wang","year":"2016","unstructured":"Wang, S., Xia, Y.: On the ball-constrained weighted maximin dispersion problem. SIAM J. Optim. 26, 1565\u20131588 (2016)","journal-title":"SIAM J. Optim."},{"key":"726_CR39","doi-asserted-by":"publisher","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":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-018-0726-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-018-0726-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-018-0726-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,12,11]],"date-time":"2019-12-11T19:08:42Z","timestamp":1576091322000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-018-0726-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,12]]},"references-count":39,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,2]]}},"alternative-id":["726"],"URL":"https:\/\/doi.org\/10.1007\/s10898-018-0726-y","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12,12]]},"assertion":[{"value":"22 October 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 November 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 December 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}