Solution structures of tensor complementarity problem
Xueyong WANG, Haibin CHEN, Yiju WANG
Solution structures of tensor complementarity problem
We introduce two new types of tensors called the strictly semi-monotone tensor and the range column Sufficient tensor and explore their structure properties. Based on the obtained results, we make a characterization to the solution of tensor complementarity problem.
Strictly semimonotone tensors / column sufficiency tensors / product invariance / permutation invariance
[1] |
Bai X, Huang Z,Wang Y. Global uniqueness and solvability for tensor complementarity problems. J Optim Theory Appl, 2016, 170: 1–13
CrossRef
Google scholar
|
[2] |
Bu C, Zhang X, Zhou J, Wang W, Wei Y. The inverse, rank and product of tensor. Linear Algebra Appl, 2014, 446: 269–280
CrossRef
Google scholar
|
[3] |
Che M, Qi L, Wei Y. Positive definite tensors to nonlinear complementarity problems. J Optim Theory Appl, 2016, 168: 475–487
CrossRef
Google scholar
|
[4] |
Chen H, Chen Y, Li G, Qi L. A semi-definite program approach for computing the maximum eigenvalue of a class of structured tensors and its applications in hypergraphs and copositivity test. Numer Linear Algebra Appl, 2017, https://doi.org/10.1002/nla.2125
CrossRef
Google scholar
|
[5] |
Chen H, Huang Z, Qi L. Copositivity detection of tensors: theory and algorithm. J Optim Theory Appl, 2017, 174: 746–761
CrossRef
Google scholar
|
[6] |
Chen H, Huang Z, Qi L. Copositive tensor detection and its applications in physics and hypergraphs. Comput Optim Appl, 2017, https://doi.org/10.1007/s10589-017-9938-1
CrossRef
Google scholar
|
[7] |
Chen H, Wang Y. On computing minimal H-eigenvalue of sign-structured tensors. Front Math China, 2017, 12(6): 1289–1302
CrossRef
Google scholar
|
[8] |
Chen H, Wang Y, Zhao H. A family of higher-order convergent iterative methods for computing the Moore-Penrose inverse. Appl Math Comput, 2011, 218(8): 4012–4016
CrossRef
Google scholar
|
[9] |
Cottle R, Pang J, Venkateswaran V. Sufficient matrices and linear complementarity problem. Linear Algebra Appl, 1989, 114-115: 231–249
CrossRef
Google scholar
|
[10] |
Facchinei F, Pang J. Finite Dimensional Variational Inequalities and Complementarity Problems.New York: Springer, 2003
|
[11] |
Huang Z, Qi L. Formulating an n-person noncooperative game as a tensor complementarity problem. Comput Optim Appl, 2016, 66: 1–20
|
[12] |
Jeyaraman I, Sivakumar C. Complementarity properties of singular M-matrices. Linear Algebra Appl, 2016, 510: 42–63
CrossRef
Google scholar
|
[13] |
Kolda T, Bader B. Tensor decompositions and applications. SIAM Review, 2009, 51: 455–500
CrossRef
Google scholar
|
[14] |
Ling C, He H, Qi L. On the cone eigenvalue complementarity problem for higher-order tensor. Comput Optim Appl, 2016, 63: 1–26
CrossRef
Google scholar
|
[15] |
Luo Z, Qi L, Xiu N. The sparsest solutions to Z-tensor complementarity problem. Optim Lett, 2015, 11: 471–482
CrossRef
Google scholar
|
[16] |
Qi L, Wang F, Wang Y. Z-eigenvalue methods for a global polynomial optimization problem. Math Program, 2009, 118: 301–316
CrossRef
Google scholar
|
[17] |
Qi L, Wang Y, Wu Ed X. D-eigenvalues of diffusion kurtosis tensors. J Comput Appl Math, 2008, 221: 150–157
CrossRef
Google scholar
|
[18] |
Qi L, Yu G, Wu E. Higher order positive semi-definite diffusion tensor imaging. SIAM J Imaging Sci, 2010, 3: 416–433
CrossRef
Google scholar
|
[19] |
Song Y, Qi L. Tensor complementarity problem and semi-positive tensor. J Optim Theory Appl, 2016, 169(3): 1069–1078
CrossRef
Google scholar
|
[20] |
Song Y, Yu G. Properties of solution set of tensor complementarity problem. J Optim Theory Appl, 2016, 170: 85–96
CrossRef
Google scholar
|
[21] |
Wang G, Zhou G, Caccetta L. Z-eigenvalue inclusion theorems for tensors. Discrete Contin Dyn Syst Ser B, 2017, 22(1): 187–198
CrossRef
Google scholar
|
[22] |
Wang Y, Caccetta L, Zhou G. Convergence analysis of a block improvement method for polynomial optimization over unit spheres. Numer Linear Algebra Appl, 2015, 22: 1059–1076
CrossRef
Google scholar
|
[23] |
Wang Y, Liu W, Caccetta L, Zhou G. Parameter selection for nonnegative l1 matrix/tensor sparse decomposition. Oper Res Lett, 2015, 43: 423–426
CrossRef
Google scholar
|
[24] |
Wang Y, Qi L, Luo S, Xu Y. An alternative steepest direction method for the optimization in evaluating geometric discord. Pac J Optim, 2014, 10: 137–149
|
[25] |
Wang Y, Qi L, Zhang X. A practical method for computing the largest M-eigenvalue of a fourth-order partially symmetric tensor. Numer Linear Algebra Appl, 2009, 16: 589–601
CrossRef
Google scholar
|
[26] |
Wang Y, Zhang K, Sun H. Criteria for strong H-tensors. Front Math China, 2016, 11: 577–592
CrossRef
Google scholar
|
[27] |
Wang Y, Zhou G, Caccetta L. Nonsingular H-tensor and its criteria. J Ind Manag Optim, 2016, 12: 1173–1186
CrossRef
Google scholar
|
[28] |
Zhang K, Wang Y. An H-tensor based iterative scheme for identifying the positive definiteness of multivariate homogeneous forms. J Comput Appl Math, 2016, 305: 1–10
CrossRef
Google scholar
|
[29] |
Zhang L, Qi L, Zhou G. M-tensors and some applications. SIAM J Matrix Anal Appl, 2014, 35: 437–452
CrossRef
Google scholar
|
[30] |
Zhang X, Ling C, Qi L. The best rank-1 approximation of a symmetric tensor and related spherical optimization problems. SIAM J Matrix Anal Appl, 2012, 33: 806–821
CrossRef
Google scholar
|
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