{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T09:14:58Z","timestamp":1780391698147,"version":"3.54.1"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2021,9,3]],"date-time":"2021-09-03T00:00:00Z","timestamp":1630627200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,9,3]],"date-time":"2021-09-03T00:00:00Z","timestamp":1630627200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1719538"],"award-info":[{"award-number":["DMS-1719538"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-1740425"],"award-info":[{"award-number":["CCF-1740425"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-11-1-0305"],"award-info":[{"award-number":["FA9550-11-1-0305"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-1565235"],"award-info":[{"award-number":["CCF-1565235"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2022,6]]},"DOI":"10.1007\/s10107-021-01696-1","type":"journal-article","created":{"date-parts":[[2021,9,3]],"date-time":"2021-09-03T20:08:13Z","timestamp":1630699693000},"page":"629-663","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["On the local stability of semidefinite relaxations"],"prefix":"10.1007","volume":"193","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0222-3761","authenticated-orcid":false,"given":"Diego","family":"Cifuentes","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sameer","family":"Agarwal","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pablo A.","family":"Parrilo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rekha R.","family":"Thomas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,9,3]]},"reference":[{"key":"1696_CR1","doi-asserted-by":"crossref","unstructured":"Aholt, C., Agarwal, S., Thomas, R.A.: QCQP approach to triangulation. In: ECCV (1), volume 7572 of Lecture Notes Computer Science, pp. 654\u2013667. Springer (2012)","DOI":"10.1007\/978-3-642-33718-5_47"},{"key":"1696_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-4848-0","volume-title":"Set-Valued Analysis","author":"J-P Aubin","year":"2009","unstructured":"Aubin, J.-P., Frankowska, H.: Set-Valued Analysis. Springer, New York (2009)"},{"key":"1696_CR3","volume-title":"Nonlinear Programming: Theory and Algorithms","author":"MS Bazaraa","year":"2013","unstructured":"Bazaraa, M.S., Sherali, H.D., Shetty, C.M.: Nonlinear Programming: Theory and Algorithms. Wiley, New York (2013)"},{"issue":"3","key":"1696_CR4","doi-asserted-by":"publisher","first-page":"844","DOI":"10.1137\/050644471","volume":"17","author":"A Beck","year":"2006","unstructured":"Beck, A., Eldar, Y.C.: Strong duality in nonconvex quadratic optimization with two quadratic constraints. SIAM J. Optim. 17(3), 844\u2013860 (2006)","journal-title":"SIAM J. Optim."},{"key":"1696_CR5","doi-asserted-by":"crossref","unstructured":"Biswas, P., Ye, Y.: Semidefinite programming for ad hoc wireless sensor network localization. In: Proceedings of International Symposium on Information Processing in Sensor Networks, pp. 46\u201354. ACM (2004)","DOI":"10.1145\/984622.984630"},{"key":"1696_CR6","doi-asserted-by":"crossref","unstructured":"Blekherman, G., Parrilo, P.A., Thomas, R.R. editors. Semidefinite Optimization and Convex Algebraic Geometry, volume\u00a013 of Series Optim MOS-SIAM (2013)","DOI":"10.1137\/1.9781611972290"},{"key":"1696_CR7","volume-title":"Real Algebraic Geometry","author":"J Bochnak","year":"2013","unstructured":"Bochnak, J., Coste, M., Roy, M.-F.: Real Algebraic Geometry, vol. 36. Springer, New York (2013)"},{"key":"1696_CR8","volume-title":"Perturbation Analysis of Optimization Problems","author":"JF Bonnans","year":"2013","unstructured":"Bonnans, J.F., Shapiro, A.: Perturbation Analysis of Optimization Problems. Springer, New York (2013)"},{"issue":"1","key":"1696_CR9","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1016\/0146-664X(79)90082-0","volume":"9","author":"FL Bookstein","year":"1979","unstructured":"Bookstein, F.L.: Fitting conic sections to scattered data. Comput. Graph. Image Process. 9(1), 56\u201371 (1979)","journal-title":"Comput. Graph. Image Process."},{"issue":"4","key":"1696_CR10","doi-asserted-by":"publisher","first-page":"746","DOI":"10.1198\/106186001317243430","volume":"10","author":"MT Chu","year":"2001","unstructured":"Chu, M.T., Trendafilov, N.T.: The orthogonally constrained regression revisited. J. Comput. Graph Stat. 10(4), 746\u2013771 (2001)","journal-title":"J. Comput. Graph Stat."},{"issue":"2","key":"1696_CR11","doi-asserted-by":"publisher","first-page":"708","DOI":"10.1137\/19M1257640","volume":"42","author":"D Cifuentes","year":"2021","unstructured":"Cifuentes, D.: A convex relaxation to compute the nearest structured rank deficient matrix. SIAM J. Matrix Anal. Appl. 42(2), 708\u2013729 (2021)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"1696_CR12","doi-asserted-by":"crossref","unstructured":"Cifuentes, D., Harris, C., Sturmfels, S.: The geometry of SDP-exactness in quadratic optimization. Math. Program. 182, 399\u2013428 (2020)","DOI":"10.1007\/s10107-019-01399-8"},{"issue":"4","key":"1696_CR13","doi-asserted-by":"publisher","first-page":"2381","DOI":"10.1137\/15M1052548","volume":"27","author":"D Cifuentes","year":"2017","unstructured":"Cifuentes, D., Parrilo, P.A.: Sampling algebraic varieties for sum of squares programs. SIAM J. Optim. 27(4), 2381\u20132404 (2017)","journal-title":"SIAM J. Optim."},{"key":"1696_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-87821-8","volume-title":"Implicit Functions and Solution Mappings: A View from Variational Analysis","author":"AL Dontchev","year":"2009","unstructured":"Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings: A View from Variational Analysis. Springer Monographs Mathem. Springer, New York (2009)"},{"key":"1696_CR15","doi-asserted-by":"crossref","unstructured":"Eriksson, A., Olsson, C., Kahl, F., Chin, T.-J.. Rotation averaging and strong duality. In: Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 127\u2013135 (2018)","DOI":"10.1109\/CVPR.2018.00021"},{"key":"1696_CR16","unstructured":"Fazel, M.: Matrix rank minimization with applications. PhD thesis, Stanford University (2002)"},{"issue":"1","key":"1696_CR17","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1007\/BF02055196","volume":"27","author":"AV Fiacco","year":"1990","unstructured":"Fiacco, A.V., Ishizuka, Y.: Sensitivity and stability analysis for nonlinear programming. Ann. Oper. Res. 27(1), 215\u2013235 (1990)","journal-title":"Ann. Oper. Res."},{"issue":"1","key":"1696_CR18","doi-asserted-by":"publisher","first-page":"188","DOI":"10.1007\/BF01258188","volume":"9","author":"P Finsler","year":"1936","unstructured":"Finsler, P.: \u00dcber das Vorkommen definiter und semidefiniter Formen in Scharen quadratischer Formen. Comment. Math. Helv. 9(1), 188\u2013192 (1936)","journal-title":"Comment. Math. Helv."},{"key":"1696_CR19","doi-asserted-by":"crossref","unstructured":"Fredriksson, J., Olsson, C.: Simultaneous multiple rotation averaging using Lagrangian duality. In: Asian Conference on Computer Vision, pp. 245\u2013258. Springer (2012)","DOI":"10.1007\/978-3-642-37431-9_19"},{"issue":"2","key":"1696_CR20","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1016\/S0167-6377(03)00069-5","volume":"32","author":"RW Freund","year":"2004","unstructured":"Freund, R.W., Jarre, F.: A sensitivity result for semidefinite programs. Oper. Res. Lett. 32(2), 126\u2013132 (2004). https:\/\/doi.org\/10.1016\/S0167-6377(03)00069-5","journal-title":"Oper. Res. Lett."},{"issue":"4","key":"1696_CR21","doi-asserted-by":"publisher","first-page":"2097","DOI":"10.1137\/090746525","volume":"20","author":"J Gouveia","year":"2010","unstructured":"Gouveia, J., Parrilo, P., Thomas, R.: Theta bodies for polynomial ideals. SIAM J. Optim. 20(4), 2097\u20132118 (2010)","journal-title":"SIAM J. Optim."},{"key":"1696_CR22","volume-title":"Algebraic Geometry: A First Course","author":"J Harris","year":"2013","unstructured":"Harris, J.: Algebraic Geometry: A First Course, vol. 133. Springer, New York (2013)"},{"issue":"13","key":"1696_CR23","doi-asserted-by":"publisher","first-page":"1135","DOI":"10.1002\/(SICI)1099-1476(19970910)20:13<1135::AID-MMA908>3.0.CO;2-9","volume":"20","author":"A Heyden","year":"1997","unstructured":"Heyden, A., \u00c5str\u00f6m, K.: Algebraic properties of multilinear constraints. Math. Methods Appl. Sci. 20(13), 1135\u20131162 (1997)","journal-title":"Math. Methods Appl. Sci."},{"key":"1696_CR24","doi-asserted-by":"crossref","unstructured":"Kaltofen, E., Yang, Z., Zhi, L.: Approximate greatest common divisors of several polynomials with linearly constrained coefficients and singular polynomials. In: Proceedings of the 2006 International Symposium on Symbolic and Algebraic Computation, pp. 169\u2013176 (2006)","DOI":"10.1145\/1145768.1145799"},{"issue":"2","key":"1696_CR25","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1023\/A:1025794313696","volume":"26","author":"S Kim","year":"2003","unstructured":"Kim, S., Kojima, M.: Exact solutions of some nonconvex quadratic optimization problems via SDP and SOCP relaxations. Comput. Optim. Appl. 26(2), 143\u2013154 (2003)","journal-title":"Comput. Optim. Appl."},{"issue":"2","key":"1696_CR26","doi-asserted-by":"publisher","first-page":"580","DOI":"10.1137\/S1052623498348274","volume":"10","author":"AB Levy","year":"2000","unstructured":"Levy, A.B., Poliquin, R.A., Rockafellar, R.T.: Stability of locally optimal solutions. SIAM J. Optim. 10(2), 580\u2013604 (2000)","journal-title":"SIAM J. Optim."},{"issue":"3","key":"1696_CR27","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. IEEE Signal Process. Mag. 27(3), 20\u201334 (2010)","journal-title":"IEEE Signal Process. Mag."},{"issue":"3","key":"1696_CR28","doi-asserted-by":"publisher","first-page":"1810","DOI":"10.1137\/120887722","volume":"23","author":"BS Mordukhovich","year":"2013","unstructured":"Mordukhovich, B.S., Rockafellar, R.T., Sarabi, M.E.: Characterizations of full stability in constrained optimization. SIAM J. Optim. 23(3), 1810\u20131849 (2013)","journal-title":"SIAM J. Optim."},{"issue":"3","key":"1696_CR29","doi-asserted-by":"publisher","first-page":"525","DOI":"10.1007\/s101070050070","volume":"85","author":"MV Nayakkankuppam","year":"1999","unstructured":"Nayakkankuppam, M.V., Overton, M.L.: Conditioning of semidefinite programs. Math. Program. 85(3), 525\u2013540 (1999)","journal-title":"Math. Program."},{"issue":"3","key":"1696_CR30","doi-asserted-by":"publisher","first-page":"1155","DOI":"10.1137\/130935112","volume":"35","author":"J Nie","year":"2014","unstructured":"Nie, J., Wang, L.: Semidefinite relaxations for best rank-1 tensor approximations. SIAM J. Matrix Anal. Appl. 35(3), 1155\u20131179 (2014)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"3","key":"1696_CR31","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1137\/S003614450444614X","volume":"49","author":"I P\u00f3lik","year":"2007","unstructured":"P\u00f3lik, I., Terlaky, T.: A survey of the S-lemma. SIAM Rev. 49(3), 371\u2013418 (2007)","journal-title":"SIAM Rev."},{"key":"1696_CR32","volume-title":"Variational Analysis","author":"RT Rockafellar","year":"2009","unstructured":"Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis, vol. 317. Springer, New York (2009)"},{"key":"1696_CR33","unstructured":"Rosen, D., Carlone, L., Bandeira, A., Leonard, J.: A certifiably correct algorithm for synchronization over the special Euclidean group. In: International Workshop on the Algorithmic Foundations of Robotics (2016)"},{"issue":"2","key":"1696_CR34","doi-asserted-by":"publisher","first-page":"286","DOI":"10.1137\/0805016","volume":"5","author":"RJ Stern","year":"1995","unstructured":"Stern, R.J., Wolkowicz, H.: Indefinite trust region subproblems and nonsymmetric eigenvalue perturbations. SIAM J. Optim. 5(2), 286\u2013313 (1995)","journal-title":"SIAM J. Optim."},{"key":"1696_CR35","unstructured":"Viklands, T.: Algorithms for the weighted orthogonal Procrustes problem and other least squares problems. PhD thesis, Umea University, Sweden (2006)"},{"key":"1696_CR36","doi-asserted-by":"crossref","unstructured":"Waldspurger, I., d\u2019Aspremont, A., Mallat, S.: Phase recovery, maxcut and complex semidefinite programming. Math. Program. 149(1\u20132), 47\u201381 (2015)","DOI":"10.1007\/s10107-013-0738-9"},{"issue":"2","key":"1696_CR37","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1093\/imaiai\/iat005","volume":"2","author":"L Wang","year":"2013","unstructured":"Wang, L., Singer, A.: Exact and stable recovery of rotations for robust synchronization. Inf. Inference 2(2), 145\u2013193 (2013)","journal-title":"Inf. Inference"},{"issue":"1","key":"1696_CR38","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(1), 245\u2013267 (2003)","journal-title":"SIAM J. Optim."},{"issue":"3","key":"1696_CR39","doi-asserted-by":"publisher","first-page":"453","DOI":"10.1007\/s101070050006","volume":"87","author":"S Zhang","year":"2000","unstructured":"Zhang, S.: Quadratic maximization and semidefinite relaxation. Math. Program. 87(3), 453\u2013465 (2000)","journal-title":"Math. Program."},{"key":"1696_CR40","doi-asserted-by":"crossref","unstructured":"Zhao, J.: An efficient solution to non-minimal case essential matrix estimation. IEEE Trans. Pattern Anal. Mach. Intell (2020)","DOI":"10.1109\/TPAMI.2020.3030161"},{"issue":"2","key":"1696_CR41","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1007\/s10898-011-9660-y","volume":"52","author":"X Zheng","year":"2012","unstructured":"Zheng, X., Sun, X., Li, D., Xu, Y.: On zero duality gap in nonconvex quadratic programming problems. J. Global Optim. 52(2), 229\u2013242 (2012)","journal-title":"J. Global Optim."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-021-01696-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10107-021-01696-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-021-01696-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,10]],"date-time":"2022-06-10T14:27:35Z","timestamp":1654871255000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10107-021-01696-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,3]]},"references-count":41,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["1696"],"URL":"https:\/\/doi.org\/10.1007\/s10107-021-01696-1","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9,3]]},"assertion":[{"value":"31 August 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 July 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 September 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}