 首页 |  期刊介绍 |  编委会 |  投稿指南 |  期刊订阅 |  下载中心 |  留言板 |  联系我们 |  重点论文 |  在线办公 |
 计算数学 2019, Vol. 41 Issue (4): 406-418    DOI:
 论文 最新目录 | 下期目录 | 过刊浏览 | 高级检索 Previous Articles  |  Next Articles 1. 南开大学数学科学学院, 天津 300071;
2. 喀什大学数学与统计学院, 喀什 844006
A CLASS OF TENSOR EIGENVALUE COMPLEMENTARITY PROBLEM
Luo Gang1, Yang Qingzhi1,2
1. School of Mathematical Sciences, Nankai University, Tianjin 300071, China;
2. School of Mathematics and Statistics, Kashi University, Kashi 844006, China
 全文: PDF (422 KB)   HTML (1 KB)   输出: BibTeX | EndNote (RIS)      背景资料

 服务 把本文推荐给朋友 加入我的书架 加入引用管理器 E-mail Alert RSS 作者相关文章

Abstract： In this paper, we generalize the matrix eigenvalue complementarity problem which has wide application in mechanical systems. A positive semidefinite eigenvalue complementarity problem(SDPEiCP) is established using fourth-order tensor form. Some properties, like the existence of the solution, computational complexity, are studied. We show the relation between SDPEiCP and a nonlinear constrained optimization problem. A shifted power method is proposed to compute the solution of SDPEiCP at last.

 引用本文: . 一类张量特征值互补问题[J]. 计算数学, 2019, 41(4): 406-418. . A CLASS OF TENSOR EIGENVALUE COMPLEMENTARITY PROBLEM[J]. Mathematica Numerica Sinica, 2019, 41(4): 406-418.

  Adly S, Rammal H. A new method for solving second-order cone eigenvalue complementarity problems[J]. Journal of Optimization Theory and Applications, 2015, 165(2):563-585. Chen Z M, Yang Q Z, Ye L. Generalized eigenvalue complementarity problem for tensors[J]. Pacific Journal of Optimization, 2017, 13(3):527-545.  Da Costa A P, Figueiredo I N, Júdice J J, et al. A complementarity eigenproblem in the stability analysis of finite dimensional elastic systems with frictional contact[M]//Complementarity:applications, algorithms and extensions. Springer, Boston, MA, 2001:67-83. Facchinei F, Pang J S. Finite-dimensional variational inequalities and complementarity problems[M]. Springer, 2003.  Fan J Y, Nie J W, Zhou A W. Tensor eigenvalue complementarity problems[J]. Mathematical Programming, 2018,170(2):507-539. Fernandes L M, Fukushima M, Júdice J J, et al. The second-order cone eigenvalue complementarity problem[J]. Optimization Methods and Software, 2016, 31(1):24-52. Hillar C J, Lim L H. Most tensor problems are NP-hard[J]. Journal of the ACM (JACM), 2013, 60(6):45.  Hou J J, Ling C, He H J. A class of second-order cone eigenvalue complementarity problems for higher-order tensors[J]. Journal of the Operations Research Society of China, 2017, 5(1):45-64. Jiang B, Li Z, Zhang S. On cones of nonnegative quartic forms[J]. Foundations of Computational Mathematics, 2017, 17(1):161-197. Judice J J, Sherali H D, Ribeiro I M, et al. On the asymmetric eigenvalue complementarity problem[J]. Optimization Methods & Software, 2009, 24(4-5):549-568. Kolda T G, Mayo J R. Shifted power method for computing tensor eigenpairs[J]. SIAM Journal on Matrix Analysis and Applications, 2011, 32(4):1095-1124. Lavilledieu P, Seeger A. Existence de valeurs propres pour les systèmes multivoques:résultats anciens et nouveaux[J]. Ann. Sci. Math. Québec, 2001, 25:47-70. Lim L H. Singular values and eigenvalues of tensors:a variational approach[C]//1st IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, 2005. IEEE, 2005:129-132.  Ling C, He H, Qi L. On the cone eigenvalue complementarity problem for higher-order tensors[J]. Computational optimization and applications, 2016, 63(1):143-168. Martins J A C, da Costa A P. Stability of finite-dimensional nonlinear elastic systems with unilateral contact and friction[J]. International journal of solids and structures, 2000, 37(18):2519-2564. Martins J A C, Barbarin S, Raous M, et al. Dynamic stability of finite dimensional linearly elastic systems with unilateral contact and Coulomb friction[J]. Computer Methods in Applied Mechanics and Engineering, 1999, 177(3-4):289-328. Qi L. Eigenvalues of a real supersymmetric tensor[J]. Journal of Symbolic Computation, 2005, 40(6):1302-1324. Queiroz M, Judice J, Humes Jr C. The symmetric eigenvalue complementarity problem[J]. Mathematics of Computation, 2004, 73(248):1849-1863.  Seeger A. Eigenvalue analysis of equilibrium processes defined by linear complementarity conditions[J]. Linear Algebra and its Applications, 1999, 292(1-3):1-14. 没有找到本文相关文献
 Copyright 2008 计算数学 版权所有 中国科学院数学与系统科学研究院 《计算数学》编辑部 北京2719信箱 (100190) Email: gxy@lsec.cc.ac.cn 本系统由北京玛格泰克科技发展有限公司设计开发 技术支持: 010-62662699 E-mail:support@magtech.com.cn 京ICP备05002806号-10