{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T16:54:49Z","timestamp":1781110489372,"version":"3.54.1"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2009,8,21]],"date-time":"2009-08-21T00:00:00Z","timestamp":1250812800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2011,6]]},"DOI":"10.1007\/s10107-009-0304-7","type":"journal-article","created":{"date-parts":[[2009,8,20]],"date-time":"2009-08-20T07:41:09Z","timestamp":1250754069000},"page":"253-283","source":"Crossref","is-referenced-by-count":171,"title":["New results on Hermitian matrix rank-one decomposition"],"prefix":"10.1007","volume":"128","author":[{"given":"Wenbao","family":"Ai","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yongwei","family":"Huang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuzhong","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2009,8,21]]},"reference":[{"issue":"4","key":"304_CR1","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1287\/moor.1080.0331","volume":"33","author":"W. Ai","year":"2008","unstructured":"Ai W., Huang Y.W., Zhang S.: On the low rank solutions for linear matrix inequalities. Math. Oper. Res. 33(4), 965\u2013975 (2008)","journal-title":"Math. Oper. Res."},{"issue":"4","key":"304_CR2","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1137\/07070601X","volume":"19","author":"W. Ai","year":"2009","unstructured":"Ai W., Zhang S.: Strong duality for the CDT subproblem: a necessary and sufficient condition. SIAM J. Optim. 19(4), 1735\u20131756 (2009)","journal-title":"SIAM J. Optim."},{"issue":"2","key":"304_CR3","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1090\/S0002-9939-1969-0234968-6","volume":"20","author":"Y.H. Au-Yeung","year":"1969","unstructured":"Au-Yeung Y.H.: A theorem on a mapping from a sphere to the circle and the simultaneous diagonalization of two Hermitian matrices. Proc. Am. Math. Soc. 20(2), 545\u2013548 (1969)","journal-title":"Proc. Am. Math. Soc."},{"key":"304_CR4","first-page":"85","volume":"3","author":"Y.H. Au-Yeung","year":"1979","unstructured":"Au-Yeung Y.H., Poon Y.T.: A remark on the convexity and positive definiteness concerning Hermitian matrices. Southeast Asian Bull. Math. 3, 85\u201392 (1979)","journal-title":"Southeast Asian Bull. Math."},{"key":"304_CR5","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/BF02574037","volume":"12","author":"A. Barvinok","year":"1995","unstructured":"Barvinok A.: Problems of distance geometry and convex properties of quadratic maps. Discrete Comput. Geometry 12, 189\u2013202 (1995)","journal-title":"Discrete Comput. Geometry"},{"key":"304_CR6","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/s004540010074","volume":"25","author":"A. Barvinok","year":"2001","unstructured":"Barvinok A.: A remark on the rank of positive semidefinite matrices subject to affine constraints. Discrete Comput. Geometry 25, 23\u201331 (2001)","journal-title":"Discrete Comput. Geometry"},{"issue":"4","key":"304_CR7","doi-asserted-by":"crossref","first-page":"1224","DOI":"10.1137\/05064816X","volume":"17","author":"A. Beck","year":"2007","unstructured":"Beck A.: Quadratic matrix programming. SIAM J. Optim. 17(4), 1224\u20131238 (2007)","journal-title":"SIAM J. Optim."},{"key":"304_CR8","volume-title":"Convex Analysis and Optimization","author":"D.P. Bertsekas","year":"2003","unstructured":"Bertsekas D.P., Nedi\u0107 A., Ozdaglar A.E.: Convex Analysis and Optimization. Athena Scientific, Belmont (2003)"},{"key":"304_CR9","unstructured":"Bohnenblust, F.: Joint positiveness of matrices. Unpublished Manuscript"},{"key":"304_CR10","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1090\/S0002-9939-1961-0122827-1","volume":"12","author":"L. Brickman","year":"1961","unstructured":"Brickman L.: On the field of values of a matrix. Proc. Am. Math. Soc. 12, 61\u201366 (1961)","journal-title":"Proc. Am. Math. Soc."},{"key":"304_CR11","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/s101070050085","volume":"86","author":"X. Chen","year":"1997","unstructured":"Chen X., Yuan Y.X.: A note on quadratic forms. Math. Program. 86, 187\u2013197 (1997)","journal-title":"Math. Program."},{"issue":"11","key":"304_CR12","doi-asserted-by":"crossref","first-page":"5618","DOI":"10.1109\/TSP.2008.929657","volume":"56","author":"A. Maio De","year":"2008","unstructured":"De Maio A., De Nicola S., Huang Y.W., Zhang S., Farina A.: Code design to optimize radar detection performance under accuracy and similarity constraints. IEEE Trans. Signal Process. 56(11), 5618\u20135629 (2008)","journal-title":"IEEE Trans. Signal Process."},{"issue":"2","key":"304_CR13","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1109\/TSP.2008.2008249","volume":"57","author":"A. Maio De","year":"2009","unstructured":"De Maio A., De Nicola S., Huang Y.W., Zhang S., Farina A.: Adaptive detection and steering estimation in the presence of useful signal and interference mismatches. IEEE Trans. Signal Process. 57(2), 436\u2013450 (2009)","journal-title":"IEEE Trans. Signal Process."},{"key":"304_CR14","unstructured":"De Maio, A., De Nicola, S., Huang, Y.W., Palomar, D.P., Zhang, S., Farina, A.: Code design for radar STAP via optimization theory. Technical Report SEEM2009-04, Department of Systems Engineering & Engineering Management, The Chinese University of Hong Kong, Accepted for publication in IEEE Trans. Signal Process. (2009)"},{"key":"304_CR15","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1007\/BF01292610","volume":"3","author":"F. Hausdorff","year":"1919","unstructured":"Hausdorff F.: Der wertvorrat einer bilinearform. Mathematische Zeitschrift 3, 314\u2013316 (1919)","journal-title":"Mathematische Zeitschrift"},{"key":"304_CR16","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/s00245-001-0034-6","volume":"45","author":"J.-B. Hiriart-Urruty","year":"2002","unstructured":"Hiriart-Urruty J.-B., Torki M.: Permanently going back and forth between the \u201cquadratic world\u201d and the \u201cconvexity world\u201d in optimization. Appl. Math. Optim. 45, 169\u2013184 (2002)","journal-title":"Appl. Math. Optim."},{"key":"304_CR17","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511810817","volume-title":"Matrix Analysis","author":"R.A. Horn","year":"1985","unstructured":"Horn R.A., Johnson C.R.: Matrix Analysis. Cambridge University Press, Cambridge (1985)"},{"issue":"3","key":"304_CR18","doi-asserted-by":"crossref","first-page":"758","DOI":"10.1287\/moor.1070.0268","volume":"32","author":"Y.W. Huang","year":"2007","unstructured":"Huang Y.W., Zhang S.: Complex matrix decomposition and quadratic programming. Math. Oper. Res. 32(3), 758\u2013768 (2007)","journal-title":"Math. Oper. Res."},{"key":"304_CR19","volume-title":"Robust Adaptive Beamforming","author":"J. Li","year":"2006","unstructured":"Li J., Stoica P.: Robust Adaptive Beamforming. Wiley-Interscience, Hoboken (2006)"},{"issue":"9","key":"304_CR20","doi-asserted-by":"crossref","first-page":"2407","DOI":"10.1109\/TSP.2004.831998","volume":"52","author":"J. Li","year":"2004","unstructured":"Li J., Stoica P., Wang Z.: Doubly constrained robust capon beamformer. IEEE Trans. Signal Process. 52(9), 2407\u20132423 (2004)","journal-title":"IEEE Trans. Signal Process."},{"key":"304_CR21","unstructured":"Pang, J.S., Zhang, S.: The joint numerical range and quadratic optimization. Unpublished Manuscript. (2004)"},{"issue":"2","key":"304_CR22","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1287\/moor.23.2.339","volume":"23","author":"G. Pataki","year":"1998","unstructured":"Pataki G.: On the rank of extreme matrices in semidefinite programs and the multiplicity of optimal eigenvalues. Math. Oper. Res. 23(2), 339\u2013358 (1998)","journal-title":"Math. Oper. Res."},{"key":"304_CR23","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1023\/A:1021796010050","volume":"99","author":"B.T. Polyak","year":"1998","unstructured":"Polyak B.T.: Convexity of quadratic transformations and its use in control and optimization. J. Optim. Theory Appl. 99, 53\u2013583 (1998)","journal-title":"J. Optim. Theory Appl."},{"issue":"3","key":"304_CR24","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.: S-lemma: a survey. SIAM Rev. 49(3), 371\u2013418 (2007)","journal-title":"SIAM Rev."},{"key":"304_CR25","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1287\/moor.28.2.246.14485","volume":"28","author":"J.F. 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":"304_CR26","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."},{"key":"304_CR27","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1007\/BF01580852","volume":"47","author":"Y.X. Yuan","year":"1990","unstructured":"Yuan Y.X.: On a subproblem of trust region algorithms for constrained optimization. Math. Program. 47, 53\u201363 (1990)","journal-title":"Math. Program."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-009-0304-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-009-0304-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-009-0304-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T05:50:07Z","timestamp":1559109007000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-009-0304-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,8,21]]},"references-count":27,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2011,6]]}},"alternative-id":["304"],"URL":"https:\/\/doi.org\/10.1007\/s10107-009-0304-7","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,8,21]]}}}