高阶张量Pareto-特征值的若干性质

doi:10.15960/j.cnki.issn.1007-6093.2015.03.005

运筹学学报 ›› 2015, Vol. 19 ›› Issue (3): 34-41.doi: 10.15960/j.cnki.issn.1007-6093.2015.03.005

高阶张量Pareto-特征值的若干性质

徐凤¹, 凌晨^1,*

1. 杭州电子科技大学数学系，杭州, 310018

收稿日期:2015-04-18 出版日期:2015-09-15 发布日期:2015-09-15
通讯作者: 凌晨 macling@hdu.edu.cn

Some properties on Pareto-eigenvalues of higher-order tensors

XU Feng¹, LING Chen^1,*

1. Department of Mathematics, Hangzhou Dianzi University, Hangzhou, 310018, China

Received:2015-04-18 Online:2015-09-15 Published:2015-09-15

摘要/Abstract

摘要：

考虑高阶张量特征值互补问题,由于求解张量的最大Pareto-特征值是一个NP难问题,关注于Pareto-特征值的估计,并给出若干关于Z-张量和M-张量的Pareto-特征值的性质.

关键词: 高阶张量, 特征值互补, Pareto-特征值, 非负张量, M-张量

Abstract:

We consider the higher-order tensor eigenvalue complementarity problem (TEiCP). Since finding the largest Pareto-eigenvalue of tensor is NP-hard in general, in this paper we focus on studying the estimation of the Pareto-eigenvalue. We also present some properties for Pareto-eigenvalues of Z-tensors and M-tensors.

Key words: higher order tensor, eigenvalue complementarity, Pareto-eigenvalue, nonnegative tensor, M-tensor

徐凤, 凌晨. 高阶张量Pareto-特征值的若干性质[J]. 运筹学学报, 2015, 19(3): 34-41.

XU Feng, LING Chen. Some properties on Pareto-eigenvalues of higher-order tensors[J]. Operations Research Transactions, 2015, 19(3): 34-41.

参考文献

Qi L. Eigenvalues of a real supersymmetric tensor [J]. Journal of Symbolic Computation, 2005, 40: 1302-1324.

Lim L H. Singular values and eigenvalues of tensors: a variational approach [C]// Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Addaptive Processing, 2005, 1: 129-132.

Chang K C, Pearson K, Zhang T. On eigenvalue problems of real symmetric tensors [J]. Journal of Mathematical Analysis and Applications, 2009, 350: 416-422.

Bloy L, Verma R. On computing the underlying fiber directions from the diffusion orientation distribution function [R]. Medical Image Computing and Computer-Assisted Intervention, MICCAI. Heidelberg: Springer, 2008, 1-8.

Lathauwer L D, Moor B D, Vandewalle J. On the best rank-1 and rank-(R_1,R_2,\cdots,R_N) approximation of higher-order tensors [J]. SIAM Journal on Matrix Analysis and Applications, 2000, 21: 1324-1342.

Ni Q, Qi L, Wang F. An eigenvalue method for the positive definiteness identification problem [J]. IEEE Transactions on Automatic Control, 2008, 53: 1096-1107.

Adly S, Seeger A. A new method for solving Pareto eigenvalue complementarity problems [J]. Computational Optimization and Applications, 2013, 55: 703-731.

Fernandes L M, J\'{u}dice J J, Sherali H D, Fukushima M. On the computation of all eigenvalues for the eigenvalue complementarity problem [J]. Journal of Global Optimization, 2014, 59: 307-326.

Ling C, He H J, Qi L. On the cone eigenvalue complementarity problem for higherorder tensors [J]. Computational Optimization and Applications, DOI: 10.1007/s10589-015-9767-z.

Chang K C, Pearson K, Zhang T. Perron Frobenius Theorem for nonnegative tensors [J]. Communications in Mathematical Sciences, 2008, 6: 507-520.

Zhang L P, Qi L, Zhou G. M-tensors and some applications [J]. SIAM Journal on Matrix Analysis and Applications, 2014, 35: 437-452.

Yang Y, Yang Q Z. Further results for Perron-Frobenius theorem for nonnegative tensors [J]. SIAM Journal on Matrix Analysis and Applications, 2010, 31: 2517-2530.

Qi L. Symmetric nonnegative tensors and copositive tensors [J]. Linear Algebra and its Applications, 2013, 439: 228-238.

高阶张量Pareto-特征值的若干性质

Some properties on Pareto-eigenvalues of higher-order tensors

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