{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,19]],"date-time":"2025-03-19T16:08:47Z","timestamp":1742400527832,"version":"3.37.3"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2019,4,15]],"date-time":"2019-04-15T00:00:00Z","timestamp":1555286400000},"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":["11671036"],"award-info":[{"award-number":["11671036"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2020,4]]},"DOI":"10.1007\/s10898-019-00771-4","type":"journal-article","created":{"date-parts":[[2019,4,15]],"date-time":"2019-04-15T18:04:55Z","timestamp":1555351495000},"page":"709-728","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Euclidean distance matrix model for protein molecular conformation"],"prefix":"10.1007","volume":"76","author":[{"given":"Fengzhen","family":"Zhai","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1397-6200","authenticated-orcid":false,"given":"Qingna","family":"Li","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,4,15]]},"reference":[{"key":"771_CR1","volume-title":"Euclidean Distance Matrices and the Molecular Conformation Problem","author":"AY Alfakih","year":"2002","unstructured":"Alfakih, A.Y., Wolkowicz, H.: Euclidean Distance Matrices and the Molecular Conformation Problem. Faculty of Mathematics, University of Waterloo, Waterloo (2002)"},{"issue":"3","key":"771_CR2","doi-asserted-by":"publisher","first-page":"1251","DOI":"10.1137\/05062754X","volume":"30","author":"P Biswas","year":"2008","unstructured":"Biswas, P., Toh, K.C., Ye, Y.: A distributed SDP approach for large-scale noisy anchor-free graph realization with applications to molecular conformation. SIAM J. Sci. Comput. 30(3), 1251\u20131277 (2008)","journal-title":"SIAM J. Sci. Comput."},{"issue":"4","key":"771_CR3","doi-asserted-by":"publisher","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., Ye, Y., Wang, T.C.: Semidefinite programming approaches for sensor network localization with noisy distance measurements. IEEE Trans. Autom. Sci. Eng. 3(4), 360\u2013371 (2006)","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"771_CR4","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/0-387-29550-X_2","volume-title":"Multiscale Optimization Methods and Applications","author":"P Biswas","year":"2006","unstructured":"Biswas, P., Ye, Y.: A distributed method for solving semidefinite programs arising from ad hoc wireless sensor network localization. In: Hager, W.W., Pardalos, P.M., Huang, S.-J. (eds.) Multiscale Optimization Methods and Applications, pp. 69\u201384. Springer, Boston (2006)"},{"key":"771_CR5","unstructured":"Cao, M.Z., Li, Q.N.: An ordinal weighted EDM model for nonmetric multidimensional scaling: an application to image ranking. Technical report, Beijing Institute of Technology (2018)"},{"key":"771_CR6","doi-asserted-by":"publisher","DOI":"10.1201\/9781420036121","volume-title":"Multidimensional Scaling","author":"TF Cox","year":"2000","unstructured":"Cox, T.F., Cox, M.A.A.: Multidimensional Scaling, 2nd edn. Chapman and hall\/CRC, Boca Raton (2000)","edition":"2"},{"issue":"1","key":"771_CR7","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1007\/s10589-016-9858-5","volume":"66","author":"C Ding","year":"2017","unstructured":"Ding, C., Qi, H.D.: Convex Euclidean distance embedding for collaborative position localization with NLOS mitigation. Comput. Optim. Appl. 66(1), 187\u2013218 (2017)","journal-title":"Comput. Optim. Appl."},{"issue":"1\u20132","key":"771_CR8","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1007\/s10107-016-1090-7","volume":"164","author":"C Ding","year":"2017","unstructured":"Ding, C., Qi, H.D.: Convex optimization learning of faithful Euclidean distance representations in nonlinear dimensionality reduction. Math. Program. 164(1\u20132), 341\u2013381 (2017)","journal-title":"Math. Program."},{"key":"771_CR9","volume-title":"Convex Optimization and Euclidean Distance Geometry","author":"J Dattorro","year":"2005","unstructured":"Dattorro, J.: Convex Optimization and Euclidean Distance Geometry. Meboo publish Google Scholar, Palo Alto (2005)"},{"issue":"6","key":"771_CR10","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1109\/MSP.2015.2398954","volume":"32","author":"I Dokmanic","year":"2015","unstructured":"Dokmanic, I., Parhizkar, R., Ranieri, J., Vetterli, M.: Euclidean distance matrices: essential theory, algorithms, and applications. IEEE Signal Process. Mag. 32(6), 12\u201330 (2015)","journal-title":"IEEE Signal Process. Mag."},{"key":"771_CR11","unstructured":"Dai, Y.J., Yao, Z.Q., Li, Q.N., Xie, D.: Innovative posture sensing method for large engineering manipulators based on nearest Euclidean distance matrix. Technical report, Xiangtan University (2018)"},{"key":"771_CR12","series-title":"Distance Geometry","first-page":"351","volume-title":"Using a Distributed SDP Approach to Solve Simulated Protein Molecular Conformation Problems","author":"XY Fang","year":"2013","unstructured":"Fang, X.Y., Toh, K.C.: Using a Distributed SDP Approach to Solve Simulated Protein Molecular Conformation Problems. Distance Geometry, pp. 351\u2013376. Springer, New York (2013)"},{"issue":"6","key":"771_CR13","doi-asserted-by":"publisher","first-page":"927","DOI":"10.1109\/TVCG.2012.299","volume":"19","author":"ER Gansner","year":"2013","unstructured":"Gansner, E.R., Hu, Y., North, S.: A maxent-stress model for graph layout. IEEE Trans. Vis. Comput. Gr. 19(6), 927\u2013940 (2013)","journal-title":"IEEE Trans. Vis. Comput. Gr."},{"key":"771_CR14","unstructured":"Gao, Y.: Structured low rank matrix optimization problems: a penalized approach. PhD thesis, National University of Singapore, August (2010)"},{"key":"771_CR15","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1007\/s12532-014-0069-8","volume":"6","author":"KF Jiang","year":"2014","unstructured":"Jiang, K.F., Sun, D.F., Toh, K.C.: A partial proximal point algorithm for nuclear norm regularized matrix least squares problems. Math. Program. Comput. 6, 281\u2013325 (2014)","journal-title":"Math. Program. Comput."},{"issue":"1","key":"771_CR16","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1023\/A:1021336413386","volume":"25","author":"HX Huang","year":"2003","unstructured":"Huang, H.X., Liang, Z.A., Pardalos, P.M.: Some properties for the Euclidean distance matrix and positive semidefinite matrix completion problems. J. Glob. Optim. 25(1), 3\u201321 (2003)","journal-title":"J. Glob. Optim."},{"issue":"4","key":"771_CR17","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1023\/A:1026016804633","volume":"27","author":"LT Hoai An","year":"2003","unstructured":"Hoai An, L.T.: Solving large scale molecular distance geometry problems by a smoothing technique via the Gaussian transform and D.C. programming. J. Glob. Optim. 27(4), 375\u2013397 (2003)","journal-title":"J. Glob. Optim."},{"issue":"4","key":"771_CR18","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1016\/0165-6147(89)90173-9","volume":"10","author":"DD Kelder","year":"1988","unstructured":"Kelder, D.D., Gabri\u00eblle, M.: Distance geometry and molecular conformation. Trends Pharmacol. Sci. 10(4), 164 (1988)","journal-title":"Trends Pharmacol. Sci."},{"issue":"4","key":"771_CR19","doi-asserted-by":"publisher","first-page":"925","DOI":"10.1007\/s00006-015-0532-2","volume":"25","author":"C Lavor","year":"2015","unstructured":"Lavor, C., Alves, R., Figueiredo, W., Petraglia, A., Maculan, N.: Clifford algebra and the discretizable molecular distance geometry problem. Adv. Appl. Clifford Algebras 25(4), 925\u2013942 (2015)","journal-title":"Adv. Appl. Clifford Algebras"},{"issue":"2","key":"771_CR20","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/j.orl.2011.01.004","volume":"39","author":"QN Li","year":"2011","unstructured":"Li, Q.N., Li, D.H.: A projected semismooth Newton method for problems of calibrating least squares covariance matrix. Oper. Res. Lett. 39(2), 103\u2013108 (2011)","journal-title":"Oper. Res. Lett."},{"issue":"1","key":"771_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1111\/j.1475-3995.2007.00622.x","volume":"15","author":"L Liberti","year":"2008","unstructured":"Liberti, L., Lavor, C., Maculan, N.: A branch-and-prune algorithm for the molecular distance geometry problem. Int. Trans. Oper. Res. 15(1), 1\u201317 (2008)","journal-title":"Int. Trans. Oper. Res."},{"issue":"4","key":"771_CR22","first-page":"467","volume":"35","author":"QN Li","year":"2017","unstructured":"Li, Q.N., Qi, H.D.: An inexact smoothing Newton method for Euclidean distance matrix optimization under ordinal constraints. J. Comput. Math. 35(4), 467\u2013483 (2017)","journal-title":"J. Comput. Math."},{"issue":"6","key":"771_CR23","doi-asserted-by":"publisher","first-page":"4351","DOI":"10.1137\/080733103","volume":"31","author":"NHZ Leung","year":"2009","unstructured":"Leung, N.H.Z., Toh, K.C.: An SDP-based divide-and-conquer algorithm for large-scale noisy anchor-free graph realization. SIAM J. Sci. Comput. 31(6), 4351\u20134372 (2009)","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"771_CR24","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1137\/120875909","volume":"56","author":"L Liberti","year":"2014","unstructured":"Liberti, L., Lavor, C., Maculan, N., Mucherino, A.: Euclidean distance geometry and applications. Siam Rev. 56(1), 3\u201369 (2014)","journal-title":"Siam Rev."},{"key":"771_CR25","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s12532-018-0137-6","volume":"10","author":"XD Li","year":"2018","unstructured":"Li, X.D., Sun, D.F., Toh, K.C.: QSDPNAL: a two-phase proximal augmented Lagrangian method for convex quadratic semidefinite programming. Math. Program. Comput. 10, 1\u201341 (2018)","journal-title":"Math. Program. Comput."},{"key":"771_CR26","first-page":"1","volume":"16","author":"XD Li","year":"2017","unstructured":"Li, X.D., Sun, D.F., Toh, K.C.: A block symmetric Gauss\u2013Seidel decomposition theo for convex composite quadratic programming and its applications. Math. Program. 16, 1\u201324 (2017)","journal-title":"Math. Program."},{"issue":"3","key":"771_CR27","doi-asserted-by":"publisher","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(3), 219\u2013234 (1999)","journal-title":"J. Glob. Optim."},{"issue":"1","key":"771_CR28","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1137\/110849523","volume":"34","author":"HD Qi","year":"2013","unstructured":"Qi, H.D.: A semismooth Newton method for the nearest Euclidean distance matrix problem. SIAM J. Matrix Anal. Appl. 34(1), 67\u201393 (2013)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"15","key":"771_CR29","doi-asserted-by":"publisher","first-page":"3815","DOI":"10.1109\/TSP.2013.2264814","volume":"61","author":"HD Qi","year":"2013","unstructured":"Qi, H.D., Xiu, N.H., Yuan, X.M.: A lagrangian dual approach to the single-source localization problem. IEEE Trans. Signal Process. 61(15), 3815\u20133826 (2013)","journal-title":"IEEE Trans. Signal Process."},{"issue":"1\u20132","key":"771_CR30","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1007\/s10107-013-0726-0","volume":"147","author":"HD Qi","year":"2014","unstructured":"Qi, H.D., Yuan, X.M.: Computing the nearest Euclidean distance matrix with low embedding dimensions. Math. program. 147(1\u20132), 351\u2013389 (2014)","journal-title":"Math. program."},{"issue":"3","key":"771_CR31","doi-asserted-by":"publisher","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 axiomatique d\u2019une classe d\u2019espaces distanci\u00e9s vectoriellement applicable sur l\u2019espace de Hilbert\u201d. Ann. Math. 36(3), 724\u2013732 (1935)","journal-title":"Ann. Math."},{"issue":"2","key":"771_CR32","doi-asserted-by":"publisher","first-page":"1072","DOI":"10.1137\/15M1021799","volume":"26","author":"DF Sun","year":"2016","unstructured":"Sun, D.F., Toh, K.C., Yang, L.Q.: An efficient inexact ABCD method for least squares semidefinite programming. SIAM J. Optim. 26(2), 1072\u20131100 (2016)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"771_CR33","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1007\/s10107-006-0088-y","volume":"112","author":"KC Toh","year":"2008","unstructured":"Toh, K.C.: An inexact primal\u2013dual path-following algorithm for convex quadratic SDP. Math. Program. 112(1), 221\u2013254 (2008)","journal-title":"Math. Program."},{"key":"771_CR34","unstructured":"Toh, K.C.: User guide for QSDP-0\u2014a Matlab software package for convex quadratic semidefinite programming. Technical report, Department of Mathematics, National University of Singapore, Singapore (2010)"},{"issue":"2","key":"771_CR35","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1007\/s10107-002-0347-5","volume":"95","author":"RH T\u00fct\u00fcnc\u00fc","year":"2003","unstructured":"T\u00fct\u00fcnc\u00fc, R.H., Toh, K.C., Todd, M.J.: Solving semidefinite-quadratic-linear programs using SDPT3. Math. Program. Ser. B 95(2), 189\u2013217 (2003)","journal-title":"Math. Program. Ser. B"},{"key":"771_CR36","unstructured":"Wegner, M., Taubert, O., Schug, A., Meyerhenke, H.: Maxent-stress optimization of 3D biomolecular models. arXiv preprint \narXiv:1706.06805\n\n (2017)"},{"issue":"1","key":"771_CR37","doi-asserted-by":"publisher","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(1), 19\u201322 (1938)","journal-title":"Psychometrika"},{"issue":"1","key":"771_CR38","doi-asserted-by":"publisher","first-page":"1850007","DOI":"10.1142\/S0217595918500070","volume":"35","author":"PP Yu","year":"2018","unstructured":"Yu, P.P., Li, Q.N.: Ordinal distance metric learning with MDS for image ranking. Asia Pac. J. Oper. Res. 35(1), 1850007 (2018)","journal-title":"Asia Pac. J. Oper. Res."},{"issue":"1","key":"771_CR39","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1023\/A:1008244930007","volume":"11","author":"Z Zou","year":"1997","unstructured":"Zou, Z., Bird, R.H., Schnabel, R.B.: A stochastic\/perturbation global optimization algorithm for distance geometry problems. J. Glob. Optim. 11(1), 91\u2013105 (1997)","journal-title":"J. Glob. Optim."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-019-00771-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-019-00771-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-019-00771-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,13]],"date-time":"2020-04-13T23:28:17Z","timestamp":1586820497000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-019-00771-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,15]]},"references-count":39,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2020,4]]}},"alternative-id":["771"],"URL":"https:\/\/doi.org\/10.1007\/s10898-019-00771-4","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"type":"print","value":"0925-5001"},{"type":"electronic","value":"1573-2916"}],"subject":[],"published":{"date-parts":[[2019,4,15]]},"assertion":[{"value":"8 October 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 April 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 April 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}