{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T19:11:30Z","timestamp":1776280290146,"version":"3.50.1"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2015,6,6]],"date-time":"2015-06-06T00:00:00Z","timestamp":1433548800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2016,1]]},"DOI":"10.1007\/s10589-015-9767-z","type":"journal-article","created":{"date-parts":[[2015,6,5]],"date-time":"2015-06-05T04:36:24Z","timestamp":1433478984000},"page":"143-168","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":46,"title":["On the cone eigenvalue complementarity problem for higher-order tensors"],"prefix":"10.1007","volume":"63","author":[{"given":"Chen","family":"Ling","sequence":"first","affiliation":[]},{"given":"Hongjin","family":"He","sequence":"additional","affiliation":[]},{"given":"Liqun","family":"Qi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,6,6]]},"reference":[{"key":"9767_CR1","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1007\/s10589-013-9534-y","volume":"55","author":"S Adly","year":"2013","unstructured":"Adly, S., Rammal, H.: A new method for solving Pareto eigenvalue complementarity problems. Comput. Optim. Appl. 55, 703\u2013731 (2013)","journal-title":"Comput. Optim. Appl."},{"key":"9767_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-8176-4848-0","volume-title":"Set-Valued Analysis","author":"JP Aubin","year":"2009","unstructured":"Aubin, J.P., Frankowska, H.: Set-Valued Analysis. Springer, Berlin (2009)"},{"key":"9767_CR3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-3-540-85988-8_1","volume-title":"Medical Image Computing and Computer-Assisted Intervention-MICCAI 2008","author":"L Bloy","year":"2008","unstructured":"Bloy, L., Verma, R.: On computing the underlying fiber directions from the diffusion orientation distribution function. In: Metaxas, D., Axel, L., Fichtinger, G., Sz\u00e9kely, G. (eds.) Medical Image Computing and Computer-Assisted Intervention-MICCAI 2008, pp. 1\u20138. Springer, Berlin (2008)"},{"key":"9767_CR4","doi-asserted-by":"crossref","first-page":"507","DOI":"10.4310\/CMS.2008.v6.n2.a12","volume":"6","author":"KC Chang","year":"2008","unstructured":"Chang, K.C., Pearson, K., Zhang, T.: Perron-Frobenius theorem for nonnegative tensors. Commun. Math. Sci 6, 507\u2013520 (2008)","journal-title":"Commun. Math. Sci"},{"key":"9767_CR5","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1016\/j.jmaa.2008.09.067","volume":"350","author":"KC Chang","year":"2009","unstructured":"Chang, K.C., Pearson, K., Zhang, T.: On eigenvalue problems of real symmetric tensors. J. Math. Anal. Appl. 350, 416\u2013422 (2009)","journal-title":"J. Math. Anal. Appl."},{"issue":"3","key":"9767_CR6","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1007\/BF00940344","volume":"60","author":"SJ Chung","year":"1989","unstructured":"Chung, S.J.: NP-completeness of the linear complementarity problem. J. Optim. Theory Appl. 60(3), 393\u2013399 (1989)","journal-title":"J. Optim. Theory Appl."},{"key":"9767_CR7","volume-title":"Using Algebraic Geometry","author":"D Cox","year":"2005","unstructured":"Cox, D., Little, J., O\u2019Shea, D.: Using Algebraic Geometry. Springer, New York (2005)"},{"key":"9767_CR8","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/978-1-4757-3279-5_4","volume-title":"Complementarity: Applications, Algorithms and Extensions","author":"A Costa da","year":"2001","unstructured":"da Costa, A., Figueiredo, I., J\u00fadice, J., Martins, J.: A complementarity eigenproblem in the stability analysis of finite dimensional elastic systems with frictional contact. In: Ferris, M., Pang, J.S., Mangasarian, O. (eds.) Complementarity: Applications, Algorithms and Extensions, pp. 67\u201383. Kluwer, New York (2001)"},{"issue":"1","key":"9767_CR9","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/s10589-008-9167-8","volume":"45","author":"A Costa da","year":"2010","unstructured":"da Costa, A., Seeger, A.: Cone-constrained eigenvalue problems: theory and algorithms. Comput. Optim. Appl. 45(1), 25\u201357 (2010)","journal-title":"Comput. Optim. Appl."},{"key":"9767_CR10","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, New York (2003)"},{"issue":"4","key":"9767_CR11","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1137\/S0036144595285963","volume":"39","author":"M Ferris","year":"1997","unstructured":"Ferris, M., Pang, J.: Engineering and economic applications of complementarity problems. SIAM Rev. 39(4), 669\u2013713 (1997)","journal-title":"SIAM Rev."},{"issue":"1","key":"9767_CR12","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/S0377-0427(00)00413-1","volume":"123","author":"GH Golub","year":"2000","unstructured":"Golub, G.H., Van der Vorst, H.A.: Eigenvalue computation in the 20th century. J. Comput. Appl. Math. 123(1), 35\u201365 (2000)","journal-title":"J. Comput. Appl. Math."},{"key":"9767_CR13","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1080\/02331930600819985","volume":"56","author":"A Iusem","year":"2007","unstructured":"Iusem, A., Seeger, A.: On convex cones with infinitely many critical angles. Optimization 56, 115\u2013128 (2007)","journal-title":"Optimization"},{"issue":"4","key":"9767_CR14","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1007\/s11075-008-9194-7","volume":"47","author":"JJ J\u00fadice","year":"2008","unstructured":"J\u00fadice, J.J., Raydan, M., Rosa, S.S., Santos, S.A.: On the solution of the symmetric eigenvalue complementarity problem by the spectral projected gradient algorithm. Numer. Algor. 47(4), 391\u2013407 (2008)","journal-title":"Numer. Algor."},{"key":"9767_CR15","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1007\/s10589-007-9017-0","volume":"37","author":"JJ J\u00fadice","year":"2007","unstructured":"J\u00fadice, J.J., Sherali, H.D., Ribeiro, I.M.: The eigenvalue complementarity problem. Comput. Optim. Appl. 37, 139\u2013156 (2007)","journal-title":"Comput. Optim. Appl."},{"issue":"4\u20135","key":"9767_CR16","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1080\/10556780903102592","volume":"24","author":"JJ Judice","year":"2009","unstructured":"Judice, J.J., Sherali, H.D., Ribeiro, I.M., Rosa, S.S.: On the asymmetric eigenvalue complementarity problem. Optim. Method Softw. 24(4\u20135), 549\u2013568 (2009)","journal-title":"Optim. Method Softw."},{"key":"9767_CR17","first-page":"47","volume":"25","author":"P Lavilledieu","year":"2001","unstructured":"Lavilledieu, P., Seeger, A.: Existence de valeurs propres pour les systmes multivoques r\u00e9sultats anciens et nouveaux. Ann. Sci. Math. Que. 25, 47\u201370 (2001)","journal-title":"Ann. Sci. Math. Que."},{"key":"9767_CR18","unstructured":"Lim, L.H.: Singular values and eigenvalues of tensors: a variational approach. In: Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Addaptive Processing. CAMSAP05, pp. 129\u2013132. IEEE Computer Society Press, Piscataway (2005)"},{"key":"9767_CR19","doi-asserted-by":"crossref","first-page":"1090","DOI":"10.1137\/09074838X","volume":"31","author":"M Ng","year":"2009","unstructured":"Ng, M., Qi, L., Zhou, G.: Finding the largest eigenvalue of a non-negative tensor. SIAM J. Matrix Anal. Appl. 31, 1090\u20131099 (2009)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"6","key":"9767_CR20","doi-asserted-by":"crossref","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(6), 1302\u20131324 (2005)","journal-title":"J. Symb. Comput."},{"issue":"1","key":"9767_CR21","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.laa.2013.03.015","volume":"439","author":"L Qi","year":"2013","unstructured":"Qi, L.: Symmetric nonnegative tensors and copositive tensors. Linear Alg. Appl. 439(1), 228\u2013238 (2013)","journal-title":"Linear Alg. Appl."},{"issue":"4","key":"9767_CR22","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1007\/s11464-007-0031-4","volume":"2","author":"L Qi","year":"2007","unstructured":"Qi, L., Sun, W., Wang, Y.: Numerical multilinear algebra and its applications. Front. Math. China 2(4), 501\u2013526 (2007)","journal-title":"Front. Math. China"},{"issue":"2","key":"9767_CR23","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1007\/s10107-007-0193-6","volume":"118","author":"L Qi","year":"2009","unstructured":"Qi, L., Wang, F., Wang, Y.: Z-eigenvalue methods for a global polynomial optimization problem. Math. Program. 118(2), 301\u2013316 (2009)","journal-title":"Math. Program."},{"key":"9767_CR24","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1137\/090755138","volume":"3","author":"L Qi","year":"2010","unstructured":"Qi, L., Yu, G., Wu, E.X.: Higher order positive semidefinite diffusion tensor imaging. SIAM J. Imaging Sci. 3, 416\u2013433 (2010)","journal-title":"SIAM J. Imaging Sci."},{"key":"9767_CR25","doi-asserted-by":"crossref","first-page":"1849","DOI":"10.1090\/S0025-5718-03-01614-4","volume":"73","author":"M Queiroz","year":"2004","unstructured":"Queiroz, M., Judice, J., Humes Jr, C.: The symmetric eigenvalue complementarity problem. Math. Comput. 73, 1849\u20131863 (2004)","journal-title":"Math. Comput."},{"key":"9767_CR26","doi-asserted-by":"crossref","unstructured":"Rockafellar, R.: Convex processes and hamiltonian dynamical systems. Convex Analysis and Mathematical Economics. Lecture Notes in Econmics and Mathematical Systems, vol. 168, pp. 122\u2013136. Springer, Berlin (1979)","DOI":"10.1007\/978-3-642-95342-2_3"},{"issue":"1","key":"9767_CR27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0024-3795(99)00004-X","volume":"292","author":"A Seeger","year":"1999","unstructured":"Seeger, A.: Eigenvalue analysis of equilibrium processes defined by linear complementarity conditions. Linear Alg. Appl. 292(1), 1\u201314 (1999)","journal-title":"Linear Alg. Appl."},{"key":"9767_CR28","unstructured":"Song, Y., Qi, L.: Eigenvalue analysis of constrained minimization problem for homogeneous polynomial. arXiv preprint arXiv:1302.6085 (2013)"},{"key":"9767_CR29","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1080\/03081087.2013.851198","volume":"63","author":"Y Song","year":"2015","unstructured":"Song, Y., Qi, L.: Necessary and sufficient conditions for copositive tensors. Linear Multilinear A. 63, 120\u2013131 (2015)","journal-title":"Linear Multilinear A."},{"key":"9767_CR30","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970715","volume-title":"Dynamics with Inequalities: Impacts and Hard Constraints","author":"D Stewart","year":"2011","unstructured":"Stewart, D.: Dynamics with Inequalities: Impacts and Hard Constraints. SIAM, Philadelphia (2011)"},{"key":"9767_CR31","doi-asserted-by":"crossref","unstructured":"van der Vorst, H.A., Golub, G.H.: 150 years old and still alive: eigenproblems. In: The State of the Art in Numerical Analysis. Institute of Mathematics and its Applications, vol. 52, pp. 93\u2013119. Oxford University Press, New York (1997)","DOI":"10.1093\/oso\/9780198500148.003.0004"},{"key":"9767_CR32","doi-asserted-by":"crossref","first-page":"2517","DOI":"10.1137\/090778766","volume":"31","author":"Y Yang","year":"2010","unstructured":"Yang, Y., Yang, Q.: Further results for Perron-Frobenius theorem for nonnegative tensors. SIAM J. Matrix Anal. Appl. 31, 2517\u20132530 (2010)","journal-title":"SIAM J. Matrix Anal. Appl."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-015-9767-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-015-9767-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-015-9767-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,9]],"date-time":"2024-06-09T10:41:40Z","timestamp":1717929700000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-015-9767-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,6,6]]},"references-count":32,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2016,1]]}},"alternative-id":["9767"],"URL":"https:\/\/doi.org\/10.1007\/s10589-015-9767-z","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,6,6]]}}}