{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:20:09Z","timestamp":1740122409586,"version":"3.37.3"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,10,12]],"date-time":"2020-10-12T00:00:00Z","timestamp":1602460800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,10,12]],"date-time":"2020-10-12T00:00:00Z","timestamp":1602460800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11871369","11871472"],"award-info":[{"award-number":["11871369","11871472"]}],"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":[[2021,3]]},"DOI":"10.1007\/s10898-020-00954-4","type":"journal-article","created":{"date-parts":[[2020,10,12]],"date-time":"2020-10-12T02:02:38Z","timestamp":1602468158000},"page":"715-732","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A semidefinite relaxation method for second-order cone tensor eigenvalue complementarity problems"],"prefix":"10.1007","volume":"79","author":[{"given":"Lulu","family":"Cheng","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7498-6616","authenticated-orcid":false,"given":"Xinzhen","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guyan","family":"Ni","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,10,12]]},"reference":[{"key":"954_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-03718-8","volume-title":"Real Algebraic Geometry","author":"J Bochnak","year":"1998","unstructured":"Bochnak, J., Coste, M., Roy, M.-F.: Real Algebraic Geometry. Springer, Berlin (1998)"},{"key":"954_CR2","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1007\/s10589-016-9838-9","volume":"65","author":"Z Chen","year":"2016","unstructured":"Chen, Z., Qi, L.: A semismooth Newton method for tensor eigenvalue complementarity problem. Comput. Optim. Appl. 65, 109\u2013126 (2016)","journal-title":"Comput. Optim. Appl."},{"key":"954_CR3","first-page":"527","volume":"13","author":"Z Chen","year":"2017","unstructured":"Chen, Z., Yang, Q., Ye, L.: Generalized eigenvalue complementarity problem for tensors. Pac. J. Optim. 13, 527\u2013545 (2017)","journal-title":"Pac. J. Optim."},{"key":"954_CR4","doi-asserted-by":"publisher","first-page":"1582","DOI":"10.1137\/140962292","volume":"35","author":"C Cui","year":"2014","unstructured":"Cui, C., Dai, Y., Nie, J.: All real eigenvalues of symmetric tensors. SIAM J. Matrix Anal. Appl. 35, 1582\u20131601 (2014)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"954_CR5","first-page":"189","volume":"54","author":"R Curto","year":"2005","unstructured":"Curto, R., Fialkow, L.: Truncated K-moment problems in several variables. J. Oper. Theory 54, 189\u2013226 (2005)","journal-title":"J. Oper. Theory"},{"key":"954_CR6","doi-asserted-by":"publisher","first-page":"1073","DOI":"10.1137\/140975656","volume":"36","author":"W Ding","year":"2015","unstructured":"Ding, W., Wei, Y.: Generalized tensor eigenvalue problems. SIAM J. Matrix Anal. Appl. 36, 1073\u20131099 (2015)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"954_CR7","volume-title":"Finite-Dimensional Variational Inequalities and Complementarity Problems","author":"F Facchinei","year":"2003","unstructured":"Facchinei, F., Pang, J.: Finite-Dimensional Variational Inequalities and Complementarity Problems. Springer, Berlin (2003)"},{"key":"954_CR8","doi-asserted-by":"publisher","DOI":"10.1080\/10556788.2018.1528251","author":"J Fan","year":"2018","unstructured":"Fan, J., Nie, J., Zhao, R.: The maximum tensor complementarity eigenvalues. Optim. Methods Softw. (2018). https:\/\/doi.org\/10.1080\/10556788.2018.1528251","journal-title":"Optim. Methods Softw."},{"key":"954_CR9","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1007\/s10107-017-1167-y","volume":"170","author":"J Fan","year":"2018","unstructured":"Fan, J., Nie, J., Zhou, A.: Tensor eigenvalue complementarity problems. Math. Program. 170, 507\u2013539 (2018)","journal-title":"Math. Program."},{"key":"954_CR10","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1137\/S1052623400380365","volume":"12","author":"M Fukushima","year":"2002","unstructured":"Fukushima, M., Luo, Z., Tseng, P.: Smoothing functions for second-order-cone complementarity problems. SIAM J. Optim. 12, 436\u2013460 (2002)","journal-title":"SIAM J. Optim."},{"key":"954_CR11","doi-asserted-by":"publisher","first-page":"851","DOI":"10.1007\/s10208-012-9132-x","volume":"12","author":"J Helton","year":"2012","unstructured":"Helton, J., Nie, J.: A semidefinite approach for truncated K-moment problems. Found. Comput. Math. 12, 851\u2013881 (2012)","journal-title":"Found. Comput. Math."},{"key":"954_CR12","doi-asserted-by":"publisher","first-page":"761","DOI":"10.1080\/10556780802699201","volume":"24","author":"D Henrion","year":"2009","unstructured":"Henrion, D., Lasserre, J., Lofberg, Y.: GloptiPoly 3: moments, optimization and semidfinite programming. Optim. Methods Softw. 24, 761\u2013779 (2009)","journal-title":"Optim. Methods Softw."},{"key":"954_CR13","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/s40305-016-0137-z","volume":"5","author":"J Hou","year":"2017","unstructured":"Hou, J., Ling, C., He, H.: A class of second-order cone eigenvalue complementarity problems for higher-order tensors. J. Oper. Res. Soc. China 5, 45\u201364 (2017)","journal-title":"J. Oper. Res. Soc. China"},{"key":"954_CR14","doi-asserted-by":"publisher","first-page":"508","DOI":"10.1016\/j.jsc.2012.10.001","volume":"50","author":"S Hu","year":"2013","unstructured":"Hu, S., Huang, Z.-H., Ling, C., Qi, L.: On determinants and eigenvalue theory of tensors. J. Symb. Comput. 50, 508\u2013531 (2013)","journal-title":"J. Symb. Comput."},{"key":"954_CR15","doi-asserted-by":"publisher","first-page":"796","DOI":"10.1137\/S1052623400366802","volume":"11","author":"J Lasserre","year":"2001","unstructured":"Lasserre, J.: Global optimization with polynomials and the problem of moments. SIAM J. Optim. 11, 796\u2013817 (2001)","journal-title":"SIAM J. Optim."},{"key":"954_CR16","doi-asserted-by":"publisher","DOI":"10.1142\/p665","volume-title":"Moments, Positive Polynomials and Their Applications","author":"J Lasserre","year":"2009","unstructured":"Lasserre, J.: Moments, Positive Polynomials and Their Applications. Imperial College Press, London (2009)"},{"key":"954_CR17","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107447226","volume-title":"Introduction to Polynomial and Semi-algebraic Optimization","author":"J Lasserre","year":"2015","unstructured":"Lasserre, J.: Introduction to Polynomial and Semi-algebraic Optimization. Cambridge University Press, Cambridge (2015)"},{"key":"954_CR18","series-title":"IMA Volumes in Mathematics and Its Applications","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1007\/978-0-387-09686-5_7","volume-title":"Emerging Applications of Algebraic Geometry","author":"M Laurent","year":"2009","unstructured":"Laurent, M.: Sums of squares, moment matrices and optimization over polynomials. In: Putinar, M., Sullivant, S. (eds.) Emerging Applications of Algebraic Geometry. IMA Volumes in Mathematics and Its Applications, vol. 149, pp. 157\u2013270. Springer, Berlin (2009)"},{"key":"954_CR19","unstructured":"Laurent, M.: Optimization over polynomials: selected topics. In: Proceedings of the International Congress of Mathematicians, Seoul (2014)"},{"key":"954_CR20","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1007\/s10589-015-9767-z","volume":"63","author":"C Ling","year":"2016","unstructured":"Ling, C., He, H., Qi, L.: On the cone eigenvalue complementarity problem for higher-order tensors. Comput. Optim. Appl. 63, 143\u2013168 (2016)","journal-title":"Comput. Optim. Appl."},{"key":"954_CR21","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1007\/s10107-012-0589-9","volume":"142","author":"J Nie","year":"2013","unstructured":"Nie, J.: Certifying convergence of Lasserre\u2019s hierarchy via flat truncation. Math. Program. 142, 485\u2013510 (2013)","journal-title":"Math. Program."},{"key":"954_CR22","doi-asserted-by":"publisher","first-page":"1634","DOI":"10.1137\/120898772","volume":"23","author":"J Nie","year":"2013","unstructured":"Nie, J.: Polynomial optimization with real varieties. SIAM J. Optim. 23, 1634\u20131646 (2013)","journal-title":"SIAM J. Optim."},{"key":"954_CR23","doi-asserted-by":"publisher","first-page":"2902","DOI":"10.1137\/17M115308X","volume":"28","author":"J Nie","year":"2018","unstructured":"Nie, J., Yang, Z., Zhang, X.: A complete semidefinite algorithm for detecting copositive matrices and tensors. SIAM J. Optim. 28, 2902\u20132921 (2018)","journal-title":"SIAM J. Optim."},{"key":"954_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10589-017-9973-y","volume":"70","author":"J Nie","year":"2018","unstructured":"Nie, J., Zhang, X.: Real eigenvalues of nonsymmetric tensors. Comput. Optim. Appl. 70, 1\u201332 (2018)","journal-title":"Comput. Optim. Appl."},{"key":"954_CR25","doi-asserted-by":"publisher","first-page":"1302","DOI":"10.1016\/j.jsc.2005.05.007","volume":"40","author":"L Qi","year":"2005","unstructured":"Qi, L.: Eigenvalues of a real supersymmetric tensor. J. Symb. Comput. 40, 1302\u20131324 (2005)","journal-title":"J. Symb. Comput."},{"key":"954_CR26","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1080\/10556789908805766","volume":"11\u201312","author":"J Sturm","year":"1999","unstructured":"Sturm, J.: Sedumi 1.02: a matlab toolbox for optimization over symmetric cones. Optim. Methods Softw. 11\u201312, 625\u2013653 (1999)","journal-title":"Optim. Methods Softw."},{"key":"954_CR27","first-page":"34","volume":"19","author":"F Xu","year":"2015","unstructured":"Xu, F., Ling, C.: Some properties on Pareto-eigenvalues of higher-order tensors. Oper. Res. Trans. 19, 34\u201341 (2015)","journal-title":"Oper. Res. Trans."},{"key":"954_CR28","doi-asserted-by":"publisher","first-page":"1181","DOI":"10.1007\/s11075-018-0522-2","volume":"80","author":"G Yu","year":"2019","unstructured":"Yu, G., Song, Y., Xu, Y., Yu, Z.: Spectral projected gradient methods for generalized tensor eigenvalue complementarity problems. Numer. Algorithms 80, 1181\u20131201 (2019)","journal-title":"Numer. Algorithms"},{"key":"954_CR29","doi-asserted-by":"publisher","first-page":"758","DOI":"10.1080\/10556788.2018.1439489","volume":"34","author":"X Zhao","year":"2019","unstructured":"Zhao, X., Fan, J.: A semidefinite method for tensor complementarity problems. Optim. Methods Softw. 34, 758\u2013769 (2019)","journal-title":"Optim. Methods Softw."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-020-00954-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10898-020-00954-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-020-00954-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,12]],"date-time":"2021-10-12T08:17:06Z","timestamp":1634026626000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10898-020-00954-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,12]]},"references-count":29,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["954"],"URL":"https:\/\/doi.org\/10.1007\/s10898-020-00954-4","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"type":"print","value":"0925-5001"},{"type":"electronic","value":"1573-2916"}],"subject":[],"published":{"date-parts":[[2020,10,12]]},"assertion":[{"value":"10 October 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 September 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 October 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}