{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T15:21:43Z","timestamp":1761060103495,"version":"3.41.0"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2016,3,25]],"date-time":"2016-03-25T00:00:00Z","timestamp":1458864000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2016,3,25]],"date-time":"2016-03-25T00:00:00Z","timestamp":1458864000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-12-1-0317"],"award-info":[{"award-number":["FA9550-12-1-0317"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-13-1-0076"],"award-info":[{"award-number":["FA9550-13-1-0076"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000057","name":"National Institute of General Medical Sciences","doi-asserted-by":"publisher","award":["R01GM090200"],"award-info":[{"award-number":["R01GM090200"]}],"id":[{"id":"10.13039\/100000057","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["LTR DTD 06-05-2012"],"award-info":[{"award-number":["LTR DTD 06-05-2012"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2016,11]]},"DOI":"10.1007\/s10107-016-0993-7","type":"journal-article","created":{"date-parts":[[2016,3,25]],"date-time":"2016-03-25T13:24:05Z","timestamp":1458912245000},"page":"433-475","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Approximating the little Grothendieck problem over the orthogonal and unitary groups"],"prefix":"10.1007","volume":"160","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7331-7557","authenticated-orcid":false,"given":"Afonso S.","family":"Bandeira","sequence":"first","affiliation":[]},{"given":"Christopher","family":"Kennedy","sequence":"additional","affiliation":[]},{"given":"Amit","family":"Singer","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,3,25]]},"reference":[{"issue":"3","key":"993_CR1","doi-asserted-by":"publisher","first-page":"746","DOI":"10.1137\/S1052623496304700","volume":"8","author":"F Alizadeh","year":"1998","unstructured":"Alizadeh, F., Haeberly, J.-P.A., Overton, M.L.: Primal-dual interior-point methods for semidefinite programming: convergence rates, stability and numerical results. SIAM J. Optim. 8(3), 746\u2013768 (1998)","journal-title":"SIAM J. Optim."},{"key":"993_CR2","first-page":"486","volume":"163","author":"N Alon","year":"2005","unstructured":"Alon, N., Makarychev, K., Makarychev, Y., Naor, A.: Quadratic forms on graphs. Invent. Math. 163, 486\u2013493 (2005)","journal-title":"Invent. Math."},{"key":"993_CR3","doi-asserted-by":"crossref","unstructured":"Alon, N., Naor, A.: Approximating the cut-norm via Grothendieck\u2019s inequality. In: Proceedings of the 36 th ACM STOC, pp. 72\u201380. ACM Press (2004)","DOI":"10.1145\/1007352.1007371"},{"key":"993_CR4","volume-title":"Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables","author":"M Abramowitz","year":"1964","unstructured":"Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York (1964)"},{"key":"993_CR5","unstructured":"Bandeira, A.S.: Convex relaxations for certain inverse problems on graphs. Ph.D. thesis, Program in Applied and Computational Mathematics, Princeton University (2015)"},{"issue":"3","key":"993_CR6","doi-asserted-by":"publisher","first-page":"827","DOI":"10.1007\/s00220-011-1280-3","volume":"305","author":"J Briet","year":"2011","unstructured":"Briet, J., Buhrman, H., Toner, B.: A generalized Grothendieck inequality and nonlocal correlations that require high entanglement. Commun. Math. Phys. 305(3), 827\u2013843 (2011)","journal-title":"Commun. Math. Phys."},{"key":"993_CR7","doi-asserted-by":"crossref","unstructured":"Briet, J., Filho, F.M.O., Vallentin, F.: The positive semidefinite Grothendieck problem with rank constraint. In: Automata, Languages and Programming, vol. 6198 of Lecture Notes in Computer Science, pp. 31\u201342. Springer, Berlin (2010)","DOI":"10.1007\/978-3-642-14165-2_4"},{"key":"993_CR8","doi-asserted-by":"publisher","unstructured":"Briet, J., Regev, O., Saket, R.: Tight hardness of the non-commutative Grothendieck problem. In: 2015 IEEE 56th Annual Symposium on Foundations of Computer Science (FOCS), pp. 1108\u20131122. doi: 10.1109\/FOCS.2015.72 (2015)","DOI":"10.1109\/FOCS.2015.72"},{"issue":"4","key":"993_CR9","doi-asserted-by":"publisher","first-page":"1611","DOI":"10.1137\/120875338","volume":"34","author":"AS Bandeira","year":"2013","unstructured":"Bandeira, A.S., Singer, A., Spielman, D.A.: A Cheeger inequality for the graph connection Laplacian. SIAM J. Matrix Anal. Appl. 34(4), 1611\u20131630 (2013)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"993_CR10","doi-asserted-by":"publisher","first-page":"811","DOI":"10.1137\/S1052623400374756","volume":"12","author":"A Ben-Tal","year":"2002","unstructured":"Ben-Tal, A., Nemirovski, A.: On tractable approximations of uncertain linear matrix inequalities affected by interval uncertainty. SIAM J. Optim. 12, 811\u2013833 (2002)","journal-title":"SIAM J. Optim."},{"key":"993_CR11","doi-asserted-by":"crossref","unstructured":"Carlen, E.A.: Trace inequalities and quantum entropy: an introductory course. http:\/\/www.ueltschi.org\/azschool\/notes\/ericcarlen.pdf (2009)","DOI":"10.1090\/conm\/529\/10428"},{"key":"993_CR12","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511994746","volume-title":"Random Matrix Methods for Wireless Communications","author":"R Couillet","year":"2011","unstructured":"Couillet, R., Debbah, M.: Random Matrix Methods for Wireless Communications. Cambridge University Press, New York (2011)"},{"issue":"1","key":"993_CR13","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1137\/130935458","volume":"25","author":"KN Chaudhury","year":"2015","unstructured":"Chaudhury, K.N., Khoo, Y., Singer, A.: Global registration of multiple point clouds using semidefinite programming. SIAM J. Optim. 25(1), 126\u2013185 (2015)","journal-title":"SIAM J. Optim."},{"key":"993_CR14","doi-asserted-by":"crossref","unstructured":"Charikar, M., Wirth, A.: Maximizing quadratic programs: extending Grothendieck\u2019s inequality. In: Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, FOCS \u201904, pp. 54\u201360. IEEE Computer Society, Washington (2004)","DOI":"10.1109\/FOCS.2004.39"},{"issue":"1","key":"993_CR15","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1090\/S0002-9939-1955-0067841-7","volume":"6","author":"K Fan","year":"1955","unstructured":"Fan, K., Hoffman, A.J.: Some metric inequalities in the space of matrices. Proc. Am. Math. Soc. 6(1), 111\u2013116 (1955)","journal-title":"Proc. Am. Math. Soc."},{"key":"993_CR16","volume-title":"Table of Integrals, Series, and Products, Fifth Edition","author":"IS Gradshteyn","year":"1994","unstructured":"Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products, Fifth Edition, 5th edn. Academic Press, Cambridge (1994)","edition":"5"},{"key":"993_CR17","unstructured":"Grothendieck, A.: Resume de la theorie metrique des produits tensoriels topologiques. Bol. Soc. Mat. Sao Paulo, p. 179 (1996). (French)"},{"key":"993_CR18","unstructured":"Gotze, F., Tikhomirov, A.: On the rate of convergence to the Marchenko\u2013Pastur distribution. arXiv:1110.1284 [math.PR] (2011)"},{"key":"993_CR19","doi-asserted-by":"publisher","first-page":"1115","DOI":"10.1145\/227683.227684","volume":"42","author":"MX Goemans","year":"1995","unstructured":"Goemans, M.X., Williamson, D.P.: Improved apprximation algorithms for maximum cut and satisfiability problems using semidefine programming. J. Assoc. Comput. Mach. 42, 1115\u20131145 (1995)","journal-title":"J. Assoc. Comput. Mach."},{"key":"993_CR20","doi-asserted-by":"publisher","first-page":"1160","DOI":"10.1137\/0907079","volume":"7","author":"NJ Higham","year":"1986","unstructured":"Higham, N.J.: Computing the polar decomposition-with applications. SIAM J. Sci. Stat. Comput. 7, 1160\u20131174 (1986)","journal-title":"SIAM J. Sci. Stat. Comput."},{"issue":"4","key":"993_CR21","doi-asserted-by":"publisher","first-page":"192","DOI":"10.2307\/2690338","volume":"48","author":"JB Keller","year":"1975","unstructured":"Keller, J.B.: Closest unitary, orthogonal and hermitian operators to a given operator. Math. Mag. 48(4), 192\u2013197 (1975)","journal-title":"Math. Mag."},{"key":"993_CR22","doi-asserted-by":"crossref","unstructured":"Khot, S.: On the unique games conjecture (invited survey). In: Proceedings of the 2010 IEEE 25th Annual Conference on Computational Complexity, CCC \u201910, pp. 99\u2013121. IEEE Computer Society, Washington (2010)","DOI":"10.1109\/CCC.2010.19"},{"key":"993_CR23","unstructured":"Leveque, O.: Random matrices and communication systems: Wishart random matrices: marginal eigenvalue distribution. http:\/\/ipg.epfl.ch\/~leveque\/Matrix\/ (2012)"},{"key":"993_CR24","doi-asserted-by":"publisher","first-page":"1081","DOI":"10.5506\/APhysPolB.42.1081","volume":"42","author":"G Livan","year":"2011","unstructured":"Livan, G., Vivo, P.: Moments of Wishart\u2013Laguerre and Jacobi ensembles of random matrices: application to the quantum transport problem in chaotic cavities. Acta Phys. Pol. B 42, 1081 (2011)","journal-title":"Acta Phys. Pol. B"},{"key":"993_CR25","doi-asserted-by":"crossref","unstructured":"Man-Cho So, A., Zhang, J., Ye, Y.: On approximating complex quadratic optimization problems via semidefinite programming relaxations. Math. Program. 110(1), 93\u2013110 (2007)","DOI":"10.1007\/s10107-006-0064-6"},{"issue":"2\u20133","key":"993_CR26","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1007\/s10107-006-0033-0","volume":"109","author":"A Nemirovski","year":"2007","unstructured":"Nemirovski, A.: Sums of random symmetric matrices and quadratic optimization under orthogonality constraints. Math. Program. 109(2\u20133), 283\u2013317 (2007)","journal-title":"Math. Program."},{"issue":"1\u20133","key":"993_CR27","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1080\/10556789808805690","volume":"9","author":"Y Nesterov","year":"1998","unstructured":"Nesterov, Y.: Semidefinite relaxation and nonconvex quadratic optimization. Optim. Methods Softw. 9(1\u20133), 141\u2013160 (1998)","journal-title":"Optim. Methods Softw."},{"key":"993_CR28","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-8853-9","volume-title":"Introductory Lectures on Convex Optimization: A Basic Course, vol. 87 of Applied Optimization","author":"Y Nesterov","year":"2004","unstructured":"Nesterov, Y.: Introductory Lectures on Convex Optimization: A Basic Course, vol. 87 of Applied Optimization. Springer, Berlin (2004)"},{"issue":"3","key":"993_CR29","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1007\/s101070050100","volume":"86","author":"A Nemirovski","year":"1999","unstructured":"Nemirovski, A., Roos, C., Terlaky, T.: On maximization of quadratic form over intersection of ellipsoids with common center. Math. Program. 86(3), 463\u2013473 (1999)","journal-title":"Math. Program."},{"key":"993_CR30","doi-asserted-by":"crossref","unstructured":"Naor, A., Regev, O., Vidick, T.: Efficient rounding for the noncommutative Grothendieck inequality. In: Proceedings of the 45th annual ACM Symposium on Symposium on theory of computing, STOC \u201913, pp. 71\u201380. ACM, New York (2013)","DOI":"10.1145\/2488608.2488618"},{"key":"993_CR31","first-page":"237323","volume":"49","author":"G Pisier","year":"2011","unstructured":"Pisier, G.: Grothendieck\u2019s theorem, past and present. Bull. Am. Math. Soc. 49, 237323 (2011)","journal-title":"Bull. Am. Math. Soc."},{"key":"993_CR32","doi-asserted-by":"crossref","unstructured":"Raghavendra, P.: Optimal algorithms and inapproximability results for every CSP. In: Proceedings of 40th ACM STOC, pp. 245\u2013254 (2008)","DOI":"10.1145\/1374376.1374414"},{"issue":"1","key":"993_CR33","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF02289451","volume":"31","author":"PH Schonemann","year":"1966","unstructured":"Schonemann, P.H.: A generalized solution of the orthogonal procrustes problem. Psychometrika 31(1), 1\u201310 (1966)","journal-title":"Psychometrika"},{"issue":"13","key":"993_CR34","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0024-3795(00)00322-0","volume":"326","author":"J Shen","year":"2001","unstructured":"Shen, J.: On the singular values of Gaussian random matrices. Linear Algebra Appl. 326(13), 1\u201314 (2001)","journal-title":"Linear Algebra Appl."},{"issue":"1","key":"993_CR35","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1016\/j.acha.2010.02.001","volume":"30","author":"A Singer","year":"2011","unstructured":"Singer, A.: Angular synchronization by eigenvectors and semidefinite programming. Appl. Comput. Harmon. Anal. 30(1), 20\u201336 (2011)","journal-title":"Appl. Comput. Harmon. Anal."},{"issue":"1","key":"993_CR36","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/s10107-009-0330-5","volume":"130","author":"A-C So","year":"2011","unstructured":"So, A.-C.: Moment inequalities for sums of random matrices and their applications in optimization. Math. Program. 130(1), 125\u2013151 (2011)","journal-title":"Math. Program."},{"issue":"2","key":"993_CR37","doi-asserted-by":"publisher","first-page":"543","DOI":"10.1137\/090767777","volume":"4","author":"A Singer","year":"2011","unstructured":"Singer, A., Shkolnisky, Y.: Three-dimensional structure determination from common lines in Cryo-EM by eigenvectors and semidefinite programming. SIAM J. Imaging Sci. 4(2), 543\u2013572 (2011)","journal-title":"SIAM J. Imaging Sci."},{"issue":"1","key":"993_CR38","first-page":"1","volume":"1","author":"AM Tulino","year":"2004","unstructured":"Tulino, A.M., Verd\u00fa, S.: Random matrix theory and wireless communications. Commun. Inf. Theory 1(1), 1\u2013182 (2004)","journal-title":"Commun. Inf. Theory"},{"key":"993_CR39","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1137\/1038003","volume":"38","author":"L Vanderberghe","year":"1996","unstructured":"Vanderberghe, L., Boyd, S.: Semidefinite programming. SIAM Rev. 38, 49\u201395 (1996)","journal-title":"SIAM Rev."},{"key":"993_CR40","volume-title":"Chapter 5 of: Compressed Sensing, Theory and Applications","author":"R Vershynin","year":"2012","unstructured":"Vershynin, R.: Introduction to the non-asymptotic analysis of random matrices. In: Eldar, Y., Kutyniok, G. (eds.) Chapter 5 of: Compressed Sensing, Theory and Applications. Cambridge University Press, Cambridge (2012)"},{"key":"993_CR41","doi-asserted-by":"crossref","unstructured":"Wen, Z., Goldfarb, D., Scheinberg, K.: Block coordinate descent methods for semidefinite programming. In: Handbook on Semidefinite, Conic and Polynomial Optimization, vol. 166 of International Series in Operations Research & Management Science, pp. 533\u2013564. Springer, US (2012)","DOI":"10.1007\/978-1-4614-0769-0_19"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-016-0993-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-016-0993-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-016-0993-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-016-0993-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,1]],"date-time":"2025-06-01T23:47:32Z","timestamp":1748821652000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-016-0993-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3,25]]},"references-count":41,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2016,11]]}},"alternative-id":["993"],"URL":"https:\/\/doi.org\/10.1007\/s10107-016-0993-7","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"type":"print","value":"0025-5610"},{"type":"electronic","value":"1436-4646"}],"subject":[],"published":{"date-parts":[[2016,3,25]]},"assertion":[{"value":"12 February 2014","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 February 2016","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 March 2016","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}