Completely Positive Binary Tensors

References

• [1] Berman A, Shaked-Monderer N (2003) Completely Positive Matrices (World Scientific Publishing Co., Inc., River Edge, NJ).Crossref, Google Scholar
• [2] Bernardi A, Gimigliano A, Idà M (2011) Computing symmetric rank for symmetric tensors. J. Symbolic Comput. 46(1):34–53.Crossref, Google Scholar
• [3] Blekherman G (2015) Typical real ranks of binary forms. Foundations Comput. Math. 15(3):793–798.Crossref, Google Scholar
• [4] Brachat J, Comon P, Mourrain B, Tsigaridas E (2010) Symmetric tensor decomposition. Linear Algebra Appl. 433(11/12):1851–1872.Crossref, Google Scholar
• [5] Burer S (2009) On the copositive representation of binary and continuous nonconvex quadratic programs. Math. Programming 120(2):479–495.Crossref, Google Scholar
• [6] Causa A, Re R (2011) On the maximum rank of a real binary form. Annali di Matematica Pura ed Applicata 190(1):55–59.Crossref, Google Scholar
• [7] Chen H, Li G, Qi L (2016) Further results on Cauchy tensors and Hankel tensors. Appl. Math. Comput. 275:50–62.Google Scholar
• [8] Cichocki A, Zdunek R, Phan AH, Amari S (2009) Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multiway Data Analysis and Blind Source Separation (Wiley, New York).Crossref, Google Scholar
• [9] Comas G, Seiguer M (2011) On the rank of a binary form. Foundations Comput. Math. 11(1):65–78.Crossref, Google Scholar
• [10] Comon P, Ottaviani G (2012) On the typical rank of real binary forms. Linear Multilinear Algebra 60(6):657–667.Crossref, Google Scholar
• [11] Comon P, Golub G, Lim L-H, Mourrain B (2008) Symmetric tensors and symmetric tensor rank. SIAM J. Matrix Anal. Appl. 30(3):1254–1279.Crossref, Google Scholar
• [12] Curto R, Fialkow L (1991) Recursiveness, positivity, and truncated moment problems. Houston J. Math. 17(4):603–635.Google Scholar
• [13] Dickinson PJC, Gijben L (2014) On the computational complexity of membership problems for the completely positive cone and its dual. Comput. Optim. Appl. 57(2):403–415.Crossref, Google Scholar
• [14] Ding W, Qi L, Wei Y (2017) Inheritance properties and sum-of-squares decomposition of Hankel tensors: Theory and algorithms. BIT Numer. Math. 57(1):169–190.Crossref, Google Scholar
• [15] Fan J, Zhou A (2017) A semidefinite algorithm for completely positive tensor decomposition. Comput. Optim. Appl. 66(2):267–283.Crossref, Google Scholar
• [16] Kreĭn M, Nudel'man AA (1977) The Markov Moment Problem and Extremal Problems, Translations of Mathematical Monographs, vol. 50 (American Mathematical Society, Providence, RI).Crossref, Google Scholar
• [17] Landsberg JM (2012) Tensors: Geometry and applications, Graduate Studies in Mathematics, vol. 128 (American Mathematical Society, Providence, RI).Google Scholar
• [18] Lim L-H (2013) Tensors and hypermatrices. Hogben L, ed. Handbook of Linear Algebra, 2nd ed. (CRC Press, Boca Raton, FL), 1–30.Google Scholar
• [19] Luo Z, Qi L (2016) Completely positive tensors: Properties, easily checkable subclasses, and tractable relaxations. SIAM J. Matrix Anal. Appl. 37(4):1675–1698.Crossref, Google Scholar
• [20] Nie J (2014) The A-truncated K-moment problem. Foundations Comput. Math. 14(6):1243–1276.Crossref, Google Scholar
• [21] Nie J (2015) Linear optimization with cones of moments and nonnegative polynomials. Math. Programming 153(1):247–274.Crossref, Google Scholar
• [22] Nie J (2017) Generating polynomials and symmetric tensor decompositions. Foundations Comput. Math. 17(2):423–465.Crossref, Google Scholar
• [23] Nie J, Ye K (2017) Hankel tensor decompositions and ranks. arXiv:1706.03631 [math.AG].Google Scholar
• [24] Oeding L, Ottaviani G (2013) Eigenvectors of tensors and algorithms for Waring decomposition. J. Symbolic Comput. 54(1):9–35.Crossref, Google Scholar
• [25] Peña J, Vera JC, Zuluaga LF (2015) Completely positive reformulations for polynomial optimization. Math. Programming 151(2):405–431.Crossref, Google Scholar
• [26] Qi L (2015) Hankel tensors: Associated Hankel matrices and Vandermonde decomposition. Comm. Math. Sci. 13(1):113–125.Crossref, Google Scholar
• [27] Qi L, Xu C, Xu Y (2014) Nonnegative tensor factorization, completely positive tensors, and a hierarchical elimination algorithm. SIAM J. Matrix Anal. Appl. 35(4):1227–1241.Crossref, Google Scholar
• [28] Qi Y, Comon P, Lim L-H (2016) Semialgebraic geometry of nonnegative tensor rank. SIAM J. Matrix Anal. Appl. 37(4):1556–1580.Crossref, Google Scholar
• [29] Seigal A (2018) Gram determinants of real binary tensors. Linear Algebra Appl. 544:350–369.Crossref, Google Scholar
• [30] Shashua A, Hazan T (2005) Non-negative tensor factorization with applications to statistics and computer vision. Proc. 22nd Internat. Conf. Machine Learn., vol. 119 (ACM, New York), 792–799.Crossref, Google Scholar
• [31] Sturm JF (1999) Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Methods Software 11/12(1–4):625–653.Crossref, Google Scholar
• [32] Sylvester JJ (1886) Sur une extension dún théorème de clebsch relatif aux courbes du quatrième degré. C. R. Math. Acad. Sci. Paris 102:1532–1534.Google Scholar
• [33] Xu C (2016) Hankel tensors, Vandermonde tensors and their positivities. Linear Algebra Appl. 491:56–72.Crossref, Google Scholar
• [34] Xu C, Wang M, Li X (2016) Generalized Vandermonde tensors. Frontiers Math. China 11(3):593–603.Crossref, Google Scholar
• [35] Xu C, Luo Z, Qi L, Chen Z (2016) {0, 1} completely positive tensors and multi-hypergraphs. Linear Algebra Appl. 510:110–123.Crossref, Google Scholar
• [36] Zhou A, Fan J (2014) The CP-matrix completion problem. SIAM J. Matrix Anal. Appl. 35(1):127–142.Crossref, Google Scholar