Zhou, Anwa; Liu, Kun; Fan, Jinyan Semidefinite relaxation methods for tensor absolute value equations. (English) Zbl 1527.15028 SIAM J. Matrix Anal. Appl. 44, No. 4, 1667-1692 (2023). MSC: 15A69 65K05 65F45 90C22 90C26 PDFBibTeX XMLCite \textit{A. Zhou} et al., SIAM J. Matrix Anal. Appl. 44, No. 4, 1667--1692 (2023; Zbl 1527.15028) Full Text: DOI
Nie, Jiawang; Tang, Xindong; Yang, Zi; Zhong, Suhan Dehomogenization for completely positive tensors. (English) Zbl 1518.15037 Numer. Algebra Control Optim. 13, No. 2, 340-363 (2023). MSC: 15B48 15A69 90C23 PDFBibTeX XMLCite \textit{J. Nie} et al., Numer. Algebra Control Optim. 13, No. 2, 340--363 (2023; Zbl 1518.15037) Full Text: DOI arXiv
Zhao, Ruixue; Fan, Jinyan Quadratic tensor eigenvalue complementarity problems. (English) Zbl 1524.65171 J. Ind. Manag. Optim. 19, No. 4, 2986-3002 (2023). MSC: 65F15 15A18 15A69 65K05 90C22 90C33 PDFBibTeX XMLCite \textit{R. Zhao} and \textit{J. Fan}, J. Ind. Manag. Optim. 19, No. 4, 2986--3002 (2023; Zbl 1524.65171) Full Text: DOI
Dressler, Mareike; Nie, Jiawang; Yang, Zi Separability of Hermitian tensors and PSD decompositions. (English) Zbl 1512.15027 Linear Multilinear Algebra 70, No. 21, 6581-6608 (2022). MSC: 15A69 15B48 65K05 90C22 PDFBibTeX XMLCite \textit{M. Dressler} et al., Linear Multilinear Algebra 70, No. 21, 6581--6608 (2022; Zbl 1512.15027) Full Text: DOI arXiv
Ni, Guyan; Li, Ying A semidefinite relaxation method for partially symmetric tensor decomposition. (English) Zbl 1505.15025 Math. Oper. Res. 47, No. 4, 2931-2949 (2022). MSC: 15A69 41A65 14P10 90C22 PDFBibTeX XMLCite \textit{G. Ni} and \textit{Y. Li}, Math. Oper. Res. 47, No. 4, 2931--2949 (2022; Zbl 1505.15025) Full Text: DOI
Zeng, Meilan Tensor \(Z\)-eigenvalue complementarity problems. (English) Zbl 1469.90150 Comput. Optim. Appl. 78, No. 2, 559-573 (2021). MSC: 90C33 65K10 90C22 15A18 PDFBibTeX XMLCite \textit{M. Zeng}, Comput. Optim. Appl. 78, No. 2, 559--573 (2021; Zbl 1469.90150) Full Text: DOI
Fan, Jinyan; Nie, Jiawang; Zhao, Ruixue The maximum tensor complementarity eigenvalues. (English) Zbl 1467.65062 Optim. Methods Softw. 35, No. 6, 1179-1190 (2020). MSC: 65K10 15A18 65F15 90C22 PDFBibTeX XMLCite \textit{J. Fan} et al., Optim. Methods Softw. 35, No. 6, 1179--1190 (2020; Zbl 1467.65062) Full Text: DOI
Zhou, Anwa; Fan, Jinyan; Wang, Qingwen Completely positive tensors in the complex field. (English) Zbl 1447.15025 Sci. China, Math. 63, No. 6, 1219-1234 (2020). MSC: 15A69 15B48 44A60 90C22 PDFBibTeX XMLCite \textit{A. Zhou} et al., Sci. China, Math. 63, No. 6, 1219--1234 (2020; Zbl 1447.15025) Full Text: DOI
Zhou, Anwa; Fan, Jinyan; Zhou, Guangming Hermitian completely positive matrices. (English) Zbl 1448.15049 Linear Algebra Appl. 604, 187-209 (2020). MSC: 15B57 15A23 44A60 90C22 PDFBibTeX XMLCite \textit{A. Zhou} et al., Linear Algebra Appl. 604, 187--209 (2020; Zbl 1448.15049) Full Text: DOI
Zhao, Ruixue; Fan, Jinyan Higher-degree tensor eigenvalue complementarity problems. (English) Zbl 1487.65074 Comput. Optim. Appl. 75, No. 3, 799-816 (2020). Reviewer: Doina Carp (Bucureşti) MSC: 65K10 15A18 15A69 65F15 90C22 PDFBibTeX XMLCite \textit{R. Zhao} and \textit{J. Fan}, Comput. Optim. Appl. 75, No. 3, 799--816 (2020; Zbl 1487.65074) Full Text: DOI
Wang, Xiao; Zhang, Xinzhen; Zhou, Guangming SDP relaxation algorithms for \(\mathbf{P(P}_0)\)-tensor detection. (English) Zbl 1514.90229 Comput. Optim. Appl. 75, No. 3, 739-752 (2020). Reviewer: Radu Ioan Boţ (Wien) MSC: 90C33 15A69 90C22 PDFBibTeX XMLCite \textit{X. Wang} et al., Comput. Optim. Appl. 75, No. 3, 739--752 (2020; Zbl 1514.90229) Full Text: DOI
Cheng, Lulu; Zhang, Xinzhen A semidefinite relaxation method for second-order cone polynomial complementarity problems. (English) Zbl 1441.15015 Comput. Optim. Appl. 75, No. 3, 629-647 (2020). MSC: 15A69 15A18 90C22 90C33 PDFBibTeX XMLCite \textit{L. Cheng} and \textit{X. Zhang}, Comput. Optim. Appl. 75, No. 3, 629--647 (2020; Zbl 1441.15015) Full Text: DOI
Zhou, Anwa; Fan, Jinyan A hierarchy of semidefinite relaxations for completely positive tensor optimization problems. (English) Zbl 1434.90127 J. Glob. Optim. 75, No. 2, 417-437 (2019). MSC: 90C22 15A69 44A60 90C26 PDFBibTeX XMLCite \textit{A. Zhou} and \textit{J. Fan}, J. Glob. Optim. 75, No. 2, 417--437 (2019; Zbl 1434.90127) Full Text: DOI
Zhou, Anwa; Fan, Jinyan A semidefinite relaxation algorithm for checking completely positive separable matrices. (English) Zbl 1438.15032 J. Ind. Manag. Optim. 15, No. 2, 893-908 (2019). MSC: 15A23 15B48 44A60 90C22 PDFBibTeX XMLCite \textit{A. Zhou} and \textit{J. Fan}, J. Ind. Manag. Optim. 15, No. 2, 893--908 (2019; Zbl 1438.15032) Full Text: DOI
Li, Li; Zhang, Xinzhen; Huang, Zheng-Hai; Qi, Liqun Test of copositive tensors. (English) Zbl 1463.65141 J. Ind. Manag. Optim. 15, No. 2, 881-891 (2019). MSC: 65K05 90C33 15A69 PDFBibTeX XMLCite \textit{L. Li} et al., J. Ind. Manag. Optim. 15, No. 2, 881--891 (2019; Zbl 1463.65141) Full Text: DOI
Nie, Jiawang; Yang, Zi; Zhang, Xinzhen A complete semidefinite algorithm for detecting copositive matrices and tensors. (English) Zbl 1406.15026 SIAM J. Optim. 28, No. 4, 2902-2921 (2018). Reviewer: Juan Ramon Torregrosa Sanchez (Valencia) MSC: 15A69 15B48 90C22 65F30 PDFBibTeX XMLCite \textit{J. Nie} et al., SIAM J. Optim. 28, No. 4, 2902--2921 (2018; Zbl 1406.15026) Full Text: DOI arXiv
Fan, Jinyan; Nie, Jiawang; Zhou, Anwa Tensor eigenvalue complementarity problems. (English) Zbl 1427.65096 Math. Program. 170, No. 2 (A), 507-539 (2018). MSC: 65K10 15A18 65F15 90C22 90C33 PDFBibTeX XMLCite \textit{J. Fan} et al., Math. Program. 170, No. 2 (A), 507--539 (2018; Zbl 1427.65096) Full Text: DOI arXiv
Zhou, Anwa; Fan, Jinyan Completely positive tensor recovery with minimal nuclear value. (English) Zbl 1391.90465 Comput. Optim. Appl. 70, No. 2, 419-441 (2018). MSC: 90C22 90C30 15A69 65K05 PDFBibTeX XMLCite \textit{A. Zhou} and \textit{J. Fan}, Comput. Optim. Appl. 70, No. 2, 419--441 (2018; Zbl 1391.90465) Full Text: DOI
Nie, Jiawang; Zhang, Xinzhen Real eigenvalues of nonsymmetric tensors. (English) Zbl 1397.65057 Comput. Optim. Appl. 70, No. 1, 1-32 (2018). Reviewer: Drahoslava Janovská (Praha) MSC: 65F15 15A18 15A69 90C22 PDFBibTeX XMLCite \textit{J. Nie} and \textit{X. Zhang}, Comput. Optim. Appl. 70, No. 1, 1--32 (2018; Zbl 1397.65057) Full Text: DOI arXiv
Lê, Công-Trình; Du, Thị-Hòa-Bình Handelman’s Positivstellensatz for polynomial matrices positive definite on polyhedra. (English) Zbl 1408.14188 Positivity 22, No. 2, 449-460 (2018). Reviewer: Tobias Kaiser (Passau) MSC: 14P99 14Q99 14P10 52B99 15B48 PDFBibTeX XMLCite \textit{C.-T. Lê} and \textit{T.-H.-B. Du}, Positivity 22, No. 2, 449--460 (2018; Zbl 1408.14188) Full Text: DOI arXiv
Mu, Cun; Hsu, Daniel; Goldfarb, Donald Greedy approaches to symmetric orthogonal tensor decomposition. (English) Zbl 1386.15051 SIAM J. Matrix Anal. Appl. 38, No. 4, 1210-1226 (2017). MSC: 15A69 15A18 49M27 65F99 PDFBibTeX XMLCite \textit{C. Mu} et al., SIAM J. Matrix Anal. Appl. 38, No. 4, 1210--1226 (2017; Zbl 1386.15051) Full Text: DOI arXiv
Nie, Jiawang Symmetric tensor nuclear norms. (English) Zbl 1372.15023 SIAM J. Appl. Algebra Geom. 1, No. 1, 599-625 (2017). MSC: 15A69 65K05 90C22 PDFBibTeX XMLCite \textit{J. Nie}, SIAM J. Appl. Algebra Geom. 1, No. 1, 599--625 (2017; Zbl 1372.15023) Full Text: DOI arXiv
Hua, Bing; Ni, Gu-Yan; Zhang, Meng-Shi Computing geometric measure of entanglement for symmetric pure states via the Jacobian SDP relaxation technique. (English) Zbl 1371.65033 J. Oper. Res. Soc. China 5, No. 1, 111-121 (2017). MSC: 65F15 81P40 15A69 65K05 90C22 PDFBibTeX XMLCite \textit{B. Hua} et al., J. Oper. Res. Soc. China 5, No. 1, 111--121 (2017; Zbl 1371.65033) Full Text: DOI
Chen, Bilian; He, Simai; Li, Zhening; Zhang, Shuzhong On new classes of nonnegative symmetric tensors. (English) Zbl 1359.15020 SIAM J. Optim. 27, No. 1, 292-318 (2017). MSC: 15A69 15A63 15B48 PDFBibTeX XMLCite \textit{B. Chen} et al., SIAM J. Optim. 27, No. 1, 292--318 (2017; Zbl 1359.15020) Full Text: DOI
Fan, Jinyan; Zhou, Anwa A semidefinite algorithm for completely positive tensor decomposition. (English) Zbl 1366.65053 Comput. Optim. Appl. 66, No. 2, 267-283 (2017). MSC: 65F30 15A69 90C22 44A60 65K05 PDFBibTeX XMLCite \textit{J. Fan} and \textit{A. Zhou}, Comput. Optim. Appl. 66, No. 2, 267--283 (2017; Zbl 1366.65053) Full Text: DOI
Fan, Jinyan; Zhou, Anwa Computing the distance between the linear matrix pencil and the completely positive cone. (English) Zbl 1381.90064 Comput. Optim. Appl. 64, No. 3, 647-670 (2016). MSC: 90C22 15A22 15A23 44A60 90C26 90C59 65K05 PDFBibTeX XMLCite \textit{J. Fan} and \textit{A. Zhou}, Comput. Optim. Appl. 64, No. 3, 647--670 (2016; Zbl 1381.90064) Full Text: DOI
Nie, Jiawang; Zhang, Xinzhen Positive maps and separable matrices. (English) Zbl 1338.15066 SIAM J. Optim. 26, No. 2, 1236-1256 (2016). MSC: 15B48 65K05 90C22 PDFBibTeX XMLCite \textit{J. Nie} and \textit{X. Zhang}, SIAM J. Optim. 26, No. 2, 1236--1256 (2016; Zbl 1338.15066) Full Text: DOI arXiv
Chen, Yannan; Qi, Liqun; Wang, Qun Positive semi-definiteness and sum-of-squares property of fourth order four dimensional Hankel tensors. (English) Zbl 1334.15025 J. Comput. Appl. Math. 302, 356-368 (2016). MSC: 15A18 15A69 PDFBibTeX XMLCite \textit{Y. Chen} et al., J. Comput. Appl. Math. 302, 356--368 (2016; Zbl 1334.15025) Full Text: DOI arXiv
Fan, Jinyan; Zhou, Anwa The CP-matrix approximation problem. (English) Zbl 1382.90072 SIAM J. Matrix Anal. Appl. 37, No. 1, 171-194 (2016). MSC: 90C22 15A23 15B48 90C26 44A60 PDFBibTeX XMLCite \textit{J. Fan} and \textit{A. Zhou}, SIAM J. Matrix Anal. Appl. 37, No. 1, 171--194 (2016; Zbl 1382.90072) Full Text: DOI arXiv
Mu, Cun; Hsu, Daniel; Goldfarb, Donald Successive rank-one approximations for nearly orthogonally decomposable symmetric tensors. (English) Zbl 1330.15030 SIAM J. Matrix Anal. Appl. 36, No. 4, 1638-1659 (2015). MSC: 15A69 15A18 62H25 94A12 62H30 68T05 PDFBibTeX XMLCite \textit{C. Mu} et al., SIAM J. Matrix Anal. Appl. 36, No. 4, 1638--1659 (2015; Zbl 1330.15030) Full Text: DOI arXiv
Zhou, AnWa; Fan, JinYan Partially positive matrices. (English) Zbl 1327.15070 Sci. China, Math. 58, No. 10, 2245-2254 (2015). MSC: 15B48 90C22 15A23 PDFBibTeX XMLCite \textit{A. Zhou} and \textit{J. Fan}, Sci. China, Math. 58, No. 10, 2245--2254 (2015; Zbl 1327.15070) Full Text: DOI
Zhou, Anwa; Fan, Jinyan Monotonically positive matrices. (English) Zbl 1322.62147 Linear Algebra Appl. 485, 467-479 (2015). MSC: 62G30 15A23 15B48 90C22 PDFBibTeX XMLCite \textit{A. Zhou} and \textit{J. Fan}, Linear Algebra Appl. 485, 467--479 (2015; Zbl 1322.62147) Full Text: DOI
Hao, C. L.; Cui, C. F.; Dai, Y. H. A sequential subspace projection method for extreme Z-eigenvalues of supersymmetric tensors. (English) Zbl 1363.65063 Numer. Linear Algebra Appl. 22, No. 2, 283-298 (2015). MSC: 65F15 15A69 PDFBibTeX XMLCite \textit{C. L. Hao} et al., Numer. Linear Algebra Appl. 22, No. 2, 283--298 (2015; Zbl 1363.65063) Full Text: DOI
Qi, Liqun; Wang, Qun; Chen, Yannan Three dimensional strongly symmetric circulant tensors. (English) Zbl 1321.15043 Linear Algebra Appl. 482, 207-220 (2015). MSC: 15A72 15B48 15B57 15A18 PDFBibTeX XMLCite \textit{L. Qi} et al., Linear Algebra Appl. 482, 207--220 (2015; Zbl 1321.15043) Full Text: DOI arXiv
Bugarin, Florian; Bartoli, Adrien; Henrion, Didier; Lasserre, Jean-Bernard; Orteu, Jean-José; Sentenac, Thierry Rank-constrained fundamental matrix estimation by polynomial global optimization versus the eight-point algorithm. (English) Zbl 1330.68288 J. Math. Imaging Vis. 53, No. 1, 42-60 (2015). MSC: 68T45 15A45 65K05 90C26 PDFBibTeX XMLCite \textit{F. Bugarin} et al., J. Math. Imaging Vis. 53, No. 1, 42--60 (2015; Zbl 1330.68288) Full Text: DOI arXiv
Jiang, Bo; Ma, Shiqian; Zhang, Shuzhong Tensor principal component analysis via convex optimization. (English) Zbl 1312.65008 Math. Program. 150, No. 2 (A), 423-457 (2015). MSC: 65C60 62H25 15A69 90C22 PDFBibTeX XMLCite \textit{B. Jiang} et al., Math. Program. 150, No. 2 (A), 423--457 (2015; Zbl 1312.65008) Full Text: DOI arXiv
Fialkow, Lawrence A. Limits of positive flat bivariate moment matrices. (English) Zbl 1304.47023 Trans. Am. Math. Soc. 367, No. 4, 2665-2702 (2015). MSC: 47A57 44A60 42A70 30E05 15B57 15-04 47A20 PDFBibTeX XMLCite \textit{L. A. Fialkow}, Trans. Am. Math. Soc. 367, No. 4, 2665--2702 (2015; Zbl 1304.47023) Full Text: DOI
He, Simai; Li, Zhening; Zhang, Shuzhong Inhomogeneous polynomial optimization over a convex set: an approximation approach. (English) Zbl 1308.90134 Math. Comput. 84, No. 292, 715-741 (2015). MSC: 90C26 90C59 65Y20 68W25 15A69 PDFBibTeX XMLCite \textit{S. He} et al., Math. Comput. 84, No. 292, 715--741 (2015; Zbl 1308.90134) Full Text: DOI
Li, Guoyin; Qi, Liqun; Yu, Gaohang The \(Z\)-eigenvalues of a symmetric tensor and its application to spectral hypergraph theory. (English) Zbl 1313.65081 Numer. Linear Algebra Appl. 20, No. 6, 1001-1029 (2013). MSC: 65F15 15A69 05C65 PDFBibTeX XMLCite \textit{G. Li} et al., Numer. Linear Algebra Appl. 20, No. 6, 1001--1029 (2013; Zbl 1313.65081) Full Text: DOI
Chen, Bilian; He, Simai; Li, Zhening; Zhang, Shuzhong Maximum block improvement and polynomial optimization. (English) Zbl 1250.90069 SIAM J. Optim. 22, No. 1, 87-107 (2012). MSC: 90C26 90C30 15A69 49M27 PDFBibTeX XMLCite \textit{B. Chen} et al., SIAM J. Optim. 22, No. 1, 87--107 (2012; Zbl 1250.90069) Full Text: DOI
Ma, Yue; Zhi, Lihong The minimum-rank Gram matrix completion via modified fixed point continuation method. (English) Zbl 1323.65042 Leykin, Anton (ed.), Proceedings of the 36th international symposium on symbolic and algebraic computation, ISSAC 2011, San Jose, CA, USA, June 7–11, 2011. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-0675-1). 241-248 (2011). MSC: 65F30 15A83 15B48 68W30 PDFBibTeX XMLCite \textit{Y. Ma} and \textit{L. Zhi}, in: Proceedings of the 36th international symposium on symbolic and algebraic computation, ISSAC 2011, San Jose, CA, USA, June 7--11, 2011. New York, NY: Association for Computing Machinery (ACM). 241--248 (2011; Zbl 1323.65042) Full Text: DOI arXiv
Chen, Po-Wei; Chen, Bor-Sen Robust synchronization analysis in nonlinear stochastic cellular networks with time-varying delays, intracellular perturbations and intercellular noise. (English) Zbl 1218.92033 Math. Biosci. 232, No. 2, 116-134 (2011). MSC: 92C40 92C42 37N25 15A39 65C20 PDFBibTeX XMLCite \textit{P.-W. Chen} and \textit{B.-S. Chen}, Math. Biosci. 232, No. 2, 116--134 (2011; Zbl 1218.92033) Full Text: DOI
Rami, Mustapha Ait; Henrion, Didier A hierarchy of LMI inner approximations of the set of stable polynomials. (English) Zbl 1220.93029 Automatica 47, No. 7, 1455-1460 (2011). MSC: 93B51 93B35 15B48 93C05 PDFBibTeX XMLCite \textit{M. A. Rami} and \textit{D. Henrion}, Automatica 47, No. 7, 1455--1460 (2011; Zbl 1220.93029) Full Text: DOI arXiv
Tunçel, Levent Polyhedral and semidefinite programming methods in combinatorial optimization. (English) Zbl 1207.90005 Fields Institute Monographs 27. Providence, RI: American Mathematical Society (AMS); Toronto: The Fields Institute for Research in Mathematical Sciences (ISBN 978-0-8218-3352-0/hbk). x, 219 p. (2010). Reviewer: Jean-Jacques Strodiot (Namur) MSC: 90-02 90C22 90C27 90C51 15A39 68Q25 PDFBibTeX XMLCite \textit{L. Tunçel}, Polyhedral and semidefinite programming methods in combinatorial optimization. Providence, RI: American Mathematical Society (AMS); Toronto: The Fields Institute for Research in Mathematical Sciences (2010; Zbl 1207.90005) Backlinks: MO
Chen, Bor-Sen; Chen, Po-Wei On the estimation of robustness and filtering ability of dynamic biochemical networks under process delays, internal parametric perturbations and external disturbances. (English) Zbl 1178.92023 Math. Biosci. 222, No. 2, 92-108 (2009). MSC: 92C42 92C40 34K20 34K60 15A39 PDFBibTeX XMLCite \textit{B.-S. Chen} and \textit{P.-W. Chen}, Math. Biosci. 222, No. 2, 92--108 (2009; Zbl 1178.92023) Full Text: DOI
Masubuchi, Izumi; Scherer, Carsten W. A recursive algorithm of exactness verification of relaxations for robust SDPs. (English) Zbl 1180.90229 Syst. Control Lett. 58, No. 8, 592-601 (2009). MSC: 90C22 15A39 PDFBibTeX XMLCite \textit{I. Masubuchi} and \textit{C. W. Scherer}, Syst. Control Lett. 58, No. 8, 592--601 (2009; Zbl 1180.90229) Full Text: DOI
Laurent, Monique Sums of squares, moment matrices and optimization over polynomials. (English) Zbl 1163.13021 Putinar, Mihai (ed.) et al., Emerging applications of algebraic geometry. Papers of the IMA workshops Optimization and control, January 16–20, 2007 and Applications in biology, dynamics, and statistics, March 5–9, 2007, held at IMA, Minneapolis, MN, USA. New York, NY: Springer (ISBN 978-0-387-09685-8/hbk). The IMA Volumes in Mathematics and its Applications 149, 157-270 (2009). Reviewer: Yueh-er Kuo (Knoxville) MSC: 13P10 13J25 14P10 15A99 90C22 90C30 PDFBibTeX XMLCite \textit{M. Laurent}, IMA Vol. Math. Appl. 149, 157--270 (2009; Zbl 1163.13021)
Scherer, C. W. Relaxations for robust linear matrix inequality problems with verifications for exactness. (English) Zbl 1122.93063 SIAM J. Matrix Anal. Appl. 27, No. 2, 365-395 (2005). MSC: 93D09 15A39 90C22 93B52 PDFBibTeX XMLCite \textit{C. W. Scherer}, SIAM J. Matrix Anal. Appl. 27, No. 2, 365--395 (2005; Zbl 1122.93063) Full Text: DOI