{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T07:45:48Z","timestamp":1774683948080,"version":"3.50.1"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2016,12,19]],"date-time":"2016-12-19T00:00:00Z","timestamp":1482105600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of P.R. China","doi-asserted-by":"crossref","award":["11571095"],"award-info":[{"award-number":["11571095"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of P.R. China","doi-asserted-by":"crossref","award":["11601134"],"award-info":[{"award-number":["11601134"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"the Hong Kong Research Grant Council","award":["PolyU 502111"],"award-info":[{"award-number":["PolyU 502111"]}]},{"name":"the Hong Kong Research Grant Council","award":["501212"],"award-info":[{"award-number":["501212"]}]},{"name":"the Hong Kong Research Grant Council","award":["501913"],"award-info":[{"award-number":["501913"]}]},{"name":"the Hong Kong Research Grant Council","award":["15302114"],"award-info":[{"award-number":["15302114"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Optim Lett"],"published-print":{"date-parts":[[2017,10]]},"DOI":"10.1007\/s11590-016-1104-7","type":"journal-article","created":{"date-parts":[[2016,12,19]],"date-time":"2016-12-19T07:29:26Z","timestamp":1482132566000},"page":"1407-1426","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":55,"title":["Strictly semi-positive tensors and the boundedness of tensor complementarity problems"],"prefix":"10.1007","volume":"11","author":[{"given":"Yisheng","family":"Song","sequence":"first","affiliation":[]},{"given":"Liqun","family":"Qi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,12,19]]},"reference":[{"key":"1104_CR1","doi-asserted-by":"crossref","first-page":"854","DOI":"10.1007\/s10957-014-0616-5","volume":"165","author":"Y Song","year":"2015","unstructured":"Song, Y., Qi, L.: Properties of some classes of structured tensors. J. Optim. Theory Appl. 165, 854\u2013873 (2015)","journal-title":"J. Optim. Theory Appl."},{"key":"1104_CR2","unstructured":"Song, Y., Qi, L.: Properties of tensor complementarity problem and some classes of structured tensors (2014). \n                        arXiv:1412.0113v1"},{"key":"1104_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-016-9872-7","author":"Z Huang","year":"2016","unstructured":"Huang, Z., Qi, L.: Formulating an n-person noncooperative game as a tensor complementarity problem. Comput. Optim. Appl. (2016). doi:\n                        10.1007\/s10589-016-9872-7","journal-title":"Comput. Optim. Appl."},{"issue":"3","key":"1104_CR4","doi-asserted-by":"crossref","first-page":"1069","DOI":"10.1007\/s10957-015-0800-2","volume":"169","author":"Y Song","year":"2016","unstructured":"Song, Y., Qi, L.: Tensor complementarity problem and semi-positive tensors. J. Optim. Theory Appl. 169(3), 1069\u20131078 (2016)","journal-title":"J. Optim. Theory Appl."},{"key":"1104_CR5","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1007\/s10957-015-0773-1","volume":"168","author":"M Che","year":"2016","unstructured":"Che, M., Qi, L., Wei, Y.: Positive definite tensors to nonlinear complementarity problems. J. Optim. Theory Appl. 168, 475\u2013487 (2016)","journal-title":"J. Optim. Theory Appl."},{"issue":"1","key":"1104_CR6","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1007\/s10957-016-0907-0","volume":"170","author":"Y Song","year":"2016","unstructured":"Song, Y., Yu, G.: Properties of solution set of tensor complementarity problem. J. Optim. Theory Appl. 170(1), 85\u201396 (2016)","journal-title":"J. Optim. Theory Appl."},{"key":"1104_CR7","doi-asserted-by":"publisher","unstructured":"Luo, Z., Qi, L., Xiu, X.: The sparsest solutions to \n                        $$Z$$\n                        \n                            \n                                            \n                                Z\n                            \n                        \n                    -tensor complementarity problems. Optim. Lett. (2015). doi:\n                        10.1007\/s11590-016-1013-9\n                        \n                    . \n                        arXiv: 1505.00993","DOI":"10.1007\/s11590-016-1013-9"},{"key":"1104_CR8","unstructured":"Gowda, M.S., Luo, Z., Qi, L., Xiu, N.: Z-tensors and complementarity problems. 1510, 07933 (2015)"},{"key":"1104_CR9","unstructured":"Ding, W., Luo, Z., Qi, L.: P-Tensors, P\n                        $$_0$$\n                        \n                            \n                                            \n                                \n                                    \n                                    0\n                                \n                            \n                        \n                    -Tensors, and Tensor Complementarity Problem (2015). \n                        arXiv:1507.06731"},{"issue":"1","key":"1104_CR10","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1007\/s10957-016-0903-4","volume":"170","author":"X Bai","year":"2016","unstructured":"Bai, X., Huang, Z., Wang, Y.: Global uniqueness and solvability for tensor complementarity problems. J. Optim. Theory Appl. 170(1), 72\u201384 (2016)","journal-title":"J. Optim. Theory Appl."},{"issue":"4","key":"1104_CR11","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1080\/10556788.2016.1180386","volume":"31","author":"Y Wang","year":"2016","unstructured":"Wang, Y., Huang, Z., Bai, X.: Exceptionally regular tensors and tensor complementarity problems. Optim. Methods Softw. 31(4), 815\u2013828 (2016)","journal-title":"Optim. Methods Softw."},{"key":"1104_CR12","unstructured":"Huang, Z., Suo, S., Wang, J.: On Q-tensors (2015). \n                        arXiv:1509.03088"},{"issue":"3","key":"1104_CR13","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1007\/s10898-015-0343-y","volume":"64","author":"Y Song","year":"2016","unstructured":"Song, Y., Qi, L.: Eigenvalue analysis of constrained minimization problem for homogeneous polynomial. J. Global Optim. 64(3), 563\u2013575 (2016)","journal-title":"J. Global Optim."},{"key":"1104_CR14","doi-asserted-by":"crossref","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."},{"issue":"1","key":"1104_CR15","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/s10589-015-9805-x","volume":"64","author":"C Ling","year":"2016","unstructured":"Ling, C., He, H., Qi, L.: Higher-degree eigenvalue complementarity problems for tensors. Comput. Optim. Appl. 64(1), 149\u2013176 (2016)","journal-title":"Comput. Optim. Appl."},{"key":"1104_CR16","unstructured":"Chen, Z., Yang, Q., Ye, L.: Generalized eigenvalue complementarity problem for tensors. Pacific J. Optim. (2015). (to appear). \n                        arXiv:1505.02494"},{"key":"1104_CR17","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/0024-3795(90)90058-K","volume":"132","author":"R Mathias","year":"1990","unstructured":"Mathias, R., Pang, J.S.: Error bounds for the linear complementarity problem with a P-matrix. Linear Algebra Appl. 132, 123\u2013136 (1990)","journal-title":"Linear Algebra Appl."},{"issue":"4","key":"1104_CR18","doi-asserted-by":"crossref","first-page":"880","DOI":"10.1287\/moor.19.4.880","volume":"19","author":"ZQ Luo","year":"1994","unstructured":"Luo, Z.Q., Mangasarian, O.L., Ren, J., Solodov, M.V.: New error bounds for the linear complementarity problem. Math. Oper. Res. 19(4), 880\u2013892 (1994)","journal-title":"Math. Oper. Res."},{"issue":"4","key":"1104_CR19","doi-asserted-by":"crossref","first-page":"1250","DOI":"10.1137\/060653019","volume":"18","author":"XJ Chen","year":"2007","unstructured":"Chen, X.J., Xiang, S.H.: Perturbation bounds of P-matrix linear complementarity problems. SIAM J. Optim. 18(4), 1250\u20131265 (2007)","journal-title":"SIAM J. Optim."},{"key":"1104_CR20","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1007\/s10107-005-0645-9","volume":"106","author":"XJ Chen","year":"2006","unstructured":"Chen, X.J., Xiang, S.H.: Computation of error bounds for P-matrix linear complementarity problems. Math. Program. Ser. A 106, 513\u2013525 (2006)","journal-title":"Math. Program. Ser. A"},{"issue":"2","key":"1104_CR21","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/s11075-014-9950-9","volume":"70","author":"TT Chen","year":"2015","unstructured":"Chen, T.T., Li, W., Wu, X.P., Vong, S.: Error bounds for linear complementarity problems of MB-matrices. Numer. Algor. 70(2), 341\u2013356 (2015)","journal-title":"Numer. Algor."},{"key":"1104_CR22","doi-asserted-by":"crossref","first-page":"830","DOI":"10.1016\/j.laa.2010.09.049","volume":"434","author":"PF Dai","year":"2011","unstructured":"Dai, P.F.: Error bounds for linear complementarity problems of DB-matrices. Linear Algebra Appl. 434, 830\u2013840 (2011)","journal-title":"Linear Algebra Appl."},{"key":"1104_CR23","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1007\/s11075-012-9533-6","volume":"61","author":"PF Dai","year":"2012","unstructured":"Dai, P.F., Li, Y.T., Lu, C.J.: Error bounds for linear complementarity problems for SB-matrices. Numer. Algor. 61, 121\u2013139 (2012)","journal-title":"Numer. Algor."},{"key":"1104_CR24","doi-asserted-by":"crossref","first-page":"741","DOI":"10.1007\/s11075-012-9691-6","volume":"64","author":"PF Dai","year":"2013","unstructured":"Dai, P.F., Li, Y.T., Lu, C.J.: New error bounds for linear complementarity problem with an SB-matrices. Numer. Algor. 64, 741\u2013757 (2013)","journal-title":"Numer. Algor."},{"key":"1104_CR25","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1016\/j.aml.2008.09.001","volume":"22","author":"M Garc\u00eda-Esnaola","year":"2009","unstructured":"Garc\u00eda-Esnaola, M., Pe\u00f1a, J.M.: Error bounds for linear complementarity problems for B-matrices. Appl. Math. Lett. 22, 1071\u20131075 (2009)","journal-title":"Appl. Math. Lett."},{"key":"1104_CR26","doi-asserted-by":"crossref","first-page":"1379","DOI":"10.1016\/j.aml.2011.12.006","volume":"25","author":"M Garc\u00eda-Esnaola","year":"2012","unstructured":"Garc\u00eda-Esnaola, M., Pe\u00f1a, J.M.: Error bounds for linear complementarity problems involving BS-matrices. Appl. Math. Lett. 25, 1379\u20131383 (2012)","journal-title":"Appl. Math. Lett."},{"key":"1104_CR27","doi-asserted-by":"crossref","first-page":"956","DOI":"10.1016\/j.laa.2010.04.024","volume":"433","author":"M Garc\u00eda-Esnaola","year":"2010","unstructured":"Garc\u00eda-Esnaola, M., Pe\u00f1a, J.M.: A comparison of error bounds for linear complementarity problems of H-matrices. Linear Algebra Appl. 433, 956\u2013964 (2010)","journal-title":"Linear Algebra Appl."},{"issue":"2","key":"1104_CR28","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1007\/s11075-013-9786-8","volume":"67","author":"W Li","year":"2014","unstructured":"Li, W., Zheng, H.: Some new error bounds for linear complementarity problems of H-matrices. Numer. Algor. 67(2), 257\u2013269 (2014)","journal-title":"Numer. Algor."},{"key":"1104_CR29","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1007\/s10957-013-0290-z","volume":"159","author":"H Sun","year":"2013","unstructured":"Sun, H., Wang, Y.J.: Further discussion on the error bound for generalized linear complementarity problem over a polyhedral cone. J. Optim. Theory Appl. 159, 93\u2013107 (2013)","journal-title":"J. Optim. Theory Appl."},{"key":"1104_CR30","doi-asserted-by":"crossref","first-page":"348","DOI":"10.1093\/imanum\/drp026","volume":"31","author":"ZY Wang","year":"2011","unstructured":"Wang, Z.Y., Yuan, Y.X.: Componentwise error bounds for linear complementarity problems. IMA J. Numer. Anal. 31, 348\u2013357 (2011)","journal-title":"IMA J. Numer. Anal."},{"key":"1104_CR31","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 nonegative tensors and copositive tensors. Linear Algebra Appl. 439, 228\u2013238 (2013)","journal-title":"Linear Algebra Appl."},{"issue":"1","key":"1104_CR32","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 of copositive tensors. Linear Multilin. Algebra 63(1), 120\u2013131 (2015)","journal-title":"Linear Multilin. Algebra"},{"key":"1104_CR33","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. Symbol. Comput. 40, 1302\u20131324 (2005)","journal-title":"J. Symbol. Comput."},{"key":"1104_CR34","doi-asserted-by":"crossref","first-page":"1309","DOI":"10.1016\/j.jsc.2006.02.011","volume":"41","author":"L Qi","year":"2006","unstructured":"Qi, L.: Rank and eigenvalues of a supersymmetric tensor, the multivariate homogeneous polynomial and the algebraic hypersurface it defines. J. Symbol. Comput. 41, 1309\u20131327 (2006)","journal-title":"J. Symbol. Comput."},{"key":"1104_CR35","unstructured":"Lim, L.H.: Singular values and eigenvalues of tensors: a variational approach. In: Proceedings of the 1st IEEE international workshop on computational advances of multi-tensor adaptive processing, pp 129\u2013132 (2005)"},{"key":"1104_CR36","doi-asserted-by":"crossref","first-page":"1045","DOI":"10.4310\/CMS.2014.v12.n6.a3","volume":"12","author":"L Qi","year":"2014","unstructured":"Qi, L.: H\n                        $$^+$$\n                        \n                            \n                                            \n                                \n                                    \n                                    +\n                                \n                            \n                        \n                    -eigenvalues of Laplacian and signless Laplacian tensors. Commun. Math. Sci. 12, 1045\u20131064 (2014)","journal-title":"Commun. Math. Sci."},{"key":"1104_CR37","doi-asserted-by":"crossref","first-page":"1581","DOI":"10.1137\/130909135","volume":"34","author":"Y Song","year":"2013","unstructured":"Song, Y., Qi, L.: Spectral properties of positively homogeneous operators induced by higher order tensors. SIAM J. Matrix Anal. Appl. 34, 1581\u20131595 (2013)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"1104_CR38","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/S0893-9659(01)00090-8","volume":"15","author":"N Xiu","year":"2002","unstructured":"Xiu, N., Zhang, J.: A characteristic quantity of P-matrices. Appl. Math. Lett. 15, 41\u201346 (2002)","journal-title":"Appl. Math. Lett."},{"key":"1104_CR39","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."},{"key":"1104_CR40","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 Algebra Appl. 292, 1\u201314 (1999)","journal-title":"Linear Algebra Appl."},{"issue":"1","key":"1104_CR41","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/S0024-3795(03)00553-6","volume":"372","author":"A Seeger","year":"2003","unstructured":"Seeger, A., Torki, M.: On eigenvalues induced by a cone constraint. Linear Algebra Appl. 372(1), 181\u2013206 (2003)","journal-title":"Linear Algebra Appl."},{"issue":"4","key":"1104_CR42","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1137\/090750391","volume":"52","author":"JB Hiriart-Urruty","year":"2010","unstructured":"Hiriart-Urruty, J.B., Seeger, A.: A variational approach to copositive matrices. SIAM Rev. 52(4), 593\u2013629 (2010)","journal-title":"SIAM Rev."}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11590-016-1104-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-016-1104-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-016-1104-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,9,18]],"date-time":"2017-09-18T03:12:09Z","timestamp":1505704329000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11590-016-1104-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,12,19]]},"references-count":42,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2017,10]]}},"alternative-id":["1104"],"URL":"https:\/\/doi.org\/10.1007\/s11590-016-1104-7","relation":{},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"value":"1862-4472","type":"print"},{"value":"1862-4480","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,12,19]]}}}