{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:53:27Z","timestamp":1772297607621,"version":"3.50.1"},"reference-count":49,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2013,11,8]],"date-time":"2013-11-08T00:00:00Z","timestamp":1383868800000},"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":[[2014,10]]},"DOI":"10.1007\/s10107-013-0726-0","type":"journal-article","created":{"date-parts":[[2013,11,7]],"date-time":"2013-11-07T01:26:52Z","timestamp":1383787612000},"page":"351-389","source":"Crossref","is-referenced-by-count":32,"title":["Computing the nearest Euclidean distance matrix with low embedding dimensions"],"prefix":"10.1007","volume":"147","author":[{"given":"Hou-Duo","family":"Qi","sequence":"first","affiliation":[]},{"given":"Xiaoming","family":"Yuan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2013,11,8]]},"reference":[{"key":"726_CR1","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1023\/A:1008655427845","volume":"12","author":"AY Alfakih","year":"1999","unstructured":"Alfakih, A.Y., Khandani, A., Wolkowicz, H.: Solving Euclidean distance matrix completion problems via semidefinite programming. Comput. Optim. Appl. 12, 13\u201330 (1999)","journal-title":"Comput. Optim. Appl."},{"key":"726_CR2","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1093\/nar\/28.1.235","volume":"28","author":"HM Berman","year":"2000","unstructured":"Berman, H.M., Westbrook, J., Feng, Z., Gillilan, G., Bhat, T.N., Weissig, H., Shindyalov, I.N., Bourne, P.E.: The protein data bank. Nucleic Acids Res. 28, 235\u2013242 (2000)","journal-title":"Nucleic Acids Res."},{"key":"726_CR3","doi-asserted-by":"crossref","unstructured":"Biswas, P., Ye, Y.: Semidefinite programming for ad hoc wireless sensor network localization. In: Proceedings of the 3rd IPSN, Berkeley, CA, pp. 46\u201354 (2004)","DOI":"10.1145\/984622.984630"},{"key":"726_CR4","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1109\/TASE.2006.877401","volume":"3","author":"P Biswas","year":"2006","unstructured":"Biswas, P., Liang, T.-C., Toh, K.-C., Wang, T.-C., Ye, Y.: Semidefinite programming approaches for sensor network localization with noisy distance measurements. IEEE Trans. Autom. Sci. Eng. 3, 360\u2013371 (2006)","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"726_CR5","volume-title":"Modern Multidimensional Scaling: Theory and Applications, Springer Series in Statistics","author":"I Borg","year":"2005","unstructured":"Borg, I., Groenen, P.J.F.: Modern Multidimensional Scaling: Theory and Applications, Springer Series in Statistics, 2nd edn. Springer, Berlin (2005)","edition":"2"},{"key":"726_CR6","doi-asserted-by":"crossref","unstructured":"Cayton, L., Dasgupta, S.: Robust Euclidean embedding. In: Proceeding of the 23rd International Conference on Machine Learning, pp. 169\u2013176, Pittsburgh, PA (2006)","DOI":"10.1145\/1143844.1143866"},{"key":"726_CR7","unstructured":"Chu, D.I., Brown, H.C., Chu, M.T.: On least squares Euclidean distance matrix approximation and completion. Department of Mathematics, North Carolina State University, Tech. Rep. (2003)"},{"key":"726_CR8","volume-title":"Optimization and Nonsmooth Analysis","author":"FH Clarke","year":"1983","unstructured":"Clarke, F.H.: Optimization and Nonsmooth Analysis. Wiley, New York (1983)"},{"key":"726_CR9","volume-title":"Multidimensional Scaling","author":"TF Cox","year":"2001","unstructured":"Cox, T.F., Cox, M.A.A.: Multidimensional Scaling, 2nd edn. Chapman and Hall\/CRC, London (2001)","edition":"2"},{"key":"726_CR10","unstructured":"Crippen, G., Havel, T.: Distance Geometry and Molecular Conformation. Wiley, New York"},{"key":"726_CR11","volume-title":"Convex Optimization and Euclidean Distance Geometry","author":"J Dattorro","year":"2005","unstructured":"Dattorro, J.: Convex Optimization and Euclidean Distance Geometry. Meboo Publishing, USA (2005)"},{"key":"726_CR12","unstructured":"de Leeuw, J.: An alternating least squares approach to squared distance scaling, unpublished manuscript, Department of Data Theory, University of Leiden, Leiden, The Netherlands (1975)"},{"key":"726_CR13","first-page":"839","volume":"78","author":"RL Dykstra","year":"1983","unstructured":"Dykstra, R.L.: An algorithm for restricted least squares regression. J. Am. Stat. Assoc. 78, 839\u2013842 (1983)","journal-title":"J. Am. Stat. Assoc."},{"key":"726_CR14","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/BF02614077","volume":"36","author":"N Gaffke","year":"1989","unstructured":"Gaffke, N., Mathar, R.: A cyclic projection algorithm via duality. Metrika 36, 29\u201354 (1989)","journal-title":"Metrika"},{"key":"726_CR15","unstructured":"Gao, Y., Sun, D.F.: A majorized penalty approach for calibrating rank constrained correlation matrix problems. Technical Report, Department of Mathematics, National University of Singapore, March (2010)"},{"key":"726_CR16","unstructured":"Gao, Y.: Structured Low Rank Matrix Optimization Problems: A Penalty Approach, PhD Thesis, National University of Singapore (2010)"},{"key":"726_CR17","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1137\/0611042","volume":"11","author":"W Glunt","year":"1990","unstructured":"Glunt, W., Hayden, T.L., Hong, S., Wells, J.: An alternating projection algorithm for computing the nearest Euclidean distance matrix. SIAM J. Matrix Anal. Appl. 11, 589\u2013600 (1990)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"726_CR18","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1007\/BF02461553","volume":"53","author":"W Glunt","year":"1991","unstructured":"Glunt, W., Hayden, T.L., Liu, W.-M.: The embedding problem for predistance matrices. Bull. Math. Biol. 53, 769\u2013796 (1991)","journal-title":"Bull. Math. Biol."},{"key":"726_CR19","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1002\/jcc.540140115","volume":"14","author":"W Glunt","year":"1993","unstructured":"Glunt, W., Hayden, T.L., Raydan, R.: Molecular conformations from distance matrices. J. Comput. Chem. 14, 114\u2013120 (1993)","journal-title":"J. Comput. Chem."},{"key":"726_CR20","first-page":"1","volume":"7","author":"JC Gower","year":"1982","unstructured":"Gower, J.C.: Euclidean ditance geometry. Math. Sci. 7, 1\u201314 (1982)","journal-title":"Math. Sci."},{"key":"726_CR21","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/0024-3795(85)90187-9","volume":"67","author":"JC Gower","year":"1985","unstructured":"Gower, J.C.: Properties of Euclidean and non-Euclidean distance matrices. Linear Algebra Appl. 67, 81\u201397 (1985)","journal-title":"Linear Algebra Appl."},{"key":"726_CR22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01580719","volume":"40","author":"SP Han","year":"1988","unstructured":"Han, S.P.: A successive projection method. Math. Program. 40, 1\u201314 (1988)","journal-title":"Math. Program."},{"key":"726_CR23","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/0024-3795(88)90202-9","volume":"109","author":"TL Hayden","year":"1988","unstructured":"Hayden, T.L., Wells, J.: Approximation by matrices positive semidefinite on a subspace. Linear Algebra Appl. 109, 115\u2013130 (1988)","journal-title":"Linear Algebra Appl."},{"key":"726_CR24","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-02796-7","volume-title":"Convex Analysis and Minimization Algorithms I","author":"J-B Hiriart-Urruty","year":"1993","unstructured":"Hiriart-Urruty, J.-B., Lemar\u00e9chal, C.: Convex Analysis and Minimization Algorithms I. Springer, Berlin (1993)"},{"key":"726_CR25","doi-asserted-by":"crossref","unstructured":"Jiang, K.F., Sun, D., Toh, K.-C.: Solving nuclear norm regularized and semidefinite matrix least sqaures problems with linear quality constraints. In: Bezdek, K., Deze, A., Ye, Y. (eds.) Fields Institute Communications Series on Discrete Geometry and Optimization, pp. 133\u2013162 (2013)","DOI":"10.1007\/978-3-319-00200-2_9"},{"key":"726_CR26","doi-asserted-by":"crossref","first-page":"1042","DOI":"10.1137\/110847081","volume":"22","author":"KF Jiang","year":"2012","unstructured":"Jiang, K.F., Sun, D.F., Toh, K.-C.: An inexact accelerated proximal gradient method for large scale linearly constrained convex SDP. SIAM J. Optim. 22, 1042\u20131064 (2012)","journal-title":"SIAM J. Optim."},{"issue":"224","key":"726_CR27","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/0024-3795(95)00096-A","volume":"223","author":"CR Johnson","year":"1995","unstructured":"Johnson, C.R., Tarazaga, P.: Connections between the real positive semidefinite and distance matrix completion problems. Linear Algebra Appl. 223(224), 375\u2013391 (1995)","journal-title":"Linear Algebra Appl."},{"key":"726_CR28","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1137\/080713380","volume":"20","author":"S Kim","year":"2009","unstructured":"Kim, S., Kojima, M., Waki, H.: Exploiting sparsity in SDP relaxation for sensor network localization. SIAM J. Optim. 20, 192\u2013215 (2009)","journal-title":"SIAM J. Optim."},{"key":"726_CR29","doi-asserted-by":"crossref","unstructured":"Krislock, N., Wolkowicz, H.: Euclidean distance matrices and applications. In: Anjos, M., Lasserre, J. (eds.) Handbook of Semidefinite, Cone and Polynomial Optimization, pp. 879\u2013914 (2012)","DOI":"10.1007\/978-1-4614-0769-0_30"},{"key":"726_CR30","doi-asserted-by":"crossref","first-page":"2679","DOI":"10.1137\/090759392","volume":"20","author":"N Krislock","year":"2010","unstructured":"Krislock, N., Wolkowicz, H.: Explicit sensor network localization using semidefinite representations and facial reductions. SIAM J. Optim. 20, 2679\u20132708 (2010)","journal-title":"SIAM J. Optim."},{"key":"726_CR31","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/S0024-3795(97)83714-7","volume":"273","author":"M Laurent","year":"1998","unstructured":"Laurent, M.: A connection between positive semidefinite and Euclidean distance matrix completion problems. Linear Algebra Appl. 273, 9\u201322 (1998)","journal-title":"Linear Algebra Appl."},{"key":"726_CR32","first-page":"221","volume-title":"The Encyclopedia of Optimization, vol. III","author":"M Laurent","year":"2001","unstructured":"Laurent, M.: Matrix completion problem. In: Floudas, C.A., Pardalos, P.M. (eds.) The Encyclopedia of Optimization, vol. III, pp. 221\u2013229. Kluwer, Dordrecht (2001)"},{"key":"726_CR33","doi-asserted-by":"crossref","first-page":"698","DOI":"10.1016\/j.ejor.2011.11.007","volume":"219","author":"C Lavor","year":"2012","unstructured":"Lavor, C., Liberti, L., Maculan, N., Mucherino, A.: Recent advances on the discretization molecular distance geometry problem. Eur. J. Oper. Res. 219, 698\u2013706 (2012)","journal-title":"Eur. J. Oper. Res."},{"issue":"1","key":"726_CR34","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1109\/TNET.2009.2023322","volume":"18","author":"S Lee","year":"2010","unstructured":"Lee, S., Zhang, Z., Sahu, S., Saha, D.: On suitability of Euclidean embedding for host-based network coordinate systems. IEEE\/ACM Trans. Networking 18(1), 27\u201340 (2010)","journal-title":"IEEE\/ACM Trans. Networking"},{"key":"726_CR35","doi-asserted-by":"crossref","unstructured":"Liberti, L., Lavor, C., Maculan, N., Mucherino, A.: Euclidean distance geometry and applications, available from arXiv:1205:0349v1. To appear in: SIAM Review May 3 (2012)","DOI":"10.1137\/120875909"},{"key":"726_CR36","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1111\/j.1475-3995.2009.00757.x","volume":"18","author":"L Liberti","year":"2011","unstructured":"Liberti, L., Lavor, C., Mucherino, A., Maculan, N.: Molecular distance geometry methods: from continuous to discrete. Int. Trans. Oper. Res. 18, 33\u201351 (2011)","journal-title":"Int. Trans. Oper. Res."},{"key":"726_CR37","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0024-3795(85)90181-8","volume":"67","author":"R Mathar","year":"1985","unstructured":"Mathar, R.: The best Euclidean fit to a given distance matrix in prescribed dimensions. Linear Algebra Appl. 67, 1\u20136 (1985)","journal-title":"Linear Algebra Appl."},{"key":"726_CR38","unstructured":"Miao, W., Pan, S., Sun, D.: A rank-corrected procedure for matrix completion with fixed basis coefficients, Arxiv, preprint arXiv:1210.3709 (2012)"},{"key":"726_CR39","unstructured":"Miao, W.: Matrix completion procedure with fixed basis coefficients and rank regularized problems with hard constraints, PhD thesis, Department of Mathematics, National University of Singapore (2013)"},{"key":"726_CR40","doi-asserted-by":"crossref","unstructured":"Mishra, B., Meyer, G., Sepulchre, R.: Low-rank optimization for distance matrix completion. In: Proceedings of the 50th IEEE Conference on Decision and Control, December (2011)","DOI":"10.1109\/CDC.2011.6160810"},{"key":"726_CR41","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1023\/A:1008380219900","volume":"15","author":"JJ Mor\u00e9","year":"1999","unstructured":"Mor\u00e9, J.J., Wu, Z.: Distance geometry optimization for protein structures. J. Glob. Optim. 15, 219\u2013234 (1999)","journal-title":"J. Glob. Optim."},{"key":"726_CR42","doi-asserted-by":"crossref","unstructured":"Ng, T.E., Zhang, H.: Predicting Internet network distance with co-ordinates-based approaches, In: Proceedings of the IEEE INFOCOM, New York, pp. 170\u2013179, June (2002)","DOI":"10.1109\/INFCOM.2002.1019258"},{"key":"726_CR43","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1137\/110849523","volume":"34","author":"H-D Qi","year":"2013","unstructured":"Qi, H.-D.: A semismooth Newton method for the nearest Euclidean distance matrix problem. SIAM J. Matrix Anal. Appl. 34, 67\u201393 (2013)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"726_CR44","doi-asserted-by":"crossref","first-page":"724","DOI":"10.2307\/1968654","volume":"36","author":"IJ Schoenberg","year":"1935","unstructured":"Schoenberg, I.J.: Remarks to Maurice Fr\u00e9chet\u2019s article \u201cSur la d\u00e9finition axiomatque d\u2019une classe d\u2019espaces vectoriels distanci\u00e9s applicbles vectoriellement sur l\u2019espace de Hilbet\u201d. Ann. Math. 36, 724\u2013732 (1935)","journal-title":"Ann. Math."},{"key":"726_CR45","doi-asserted-by":"crossref","first-page":"2319","DOI":"10.1126\/science.290.5500.2319","volume":"290","author":"JB Tenenbaum","year":"2000","unstructured":"Tenenbaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319\u20132323 (2000)","journal-title":"Science"},{"key":"726_CR46","first-page":"221","volume":"112","author":"KC Toh","year":"2008","unstructured":"Toh, K.C.: An inexact path-following algorithm for convex quadratic SDP. Math. Program. 112, 221\u2013254 (2008)","journal-title":"Math. Program."},{"key":"726_CR47","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1023\/A:1008722907820","volume":"17","author":"MW Trosset","year":"2000","unstructured":"Trosset, M.W.: Distance matrix completion by numerical optimization. Comput. Optim. Appl. 17, 11\u201322 (2000)","journal-title":"Comput. Optim. Appl."},{"key":"726_CR48","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1137\/050640308","volume":"18","author":"P Tseng","year":"2007","unstructured":"Tseng, P.: Second-order cone programming relaxation of sensor network localization. SIAM J. Optim. 18, 156\u2013185 (2007)","journal-title":"SIAM J. Optim."},{"key":"726_CR49","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1007\/BF02287916","volume":"3","author":"G Young","year":"1938","unstructured":"Young, G., Householder, A.S.: Discussion of a set of points in terms of their mutual distances. Psychometrika 3, 19\u201322 (1938)","journal-title":"Psychometrika"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-013-0726-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-013-0726-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-013-0726-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,30]],"date-time":"2025-04-30T19:43:58Z","timestamp":1746042238000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-013-0726-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,11,8]]},"references-count":49,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2014,10]]}},"alternative-id":["726"],"URL":"https:\/\/doi.org\/10.1007\/s10107-013-0726-0","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,11,8]]}}}