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计算数学  2019, Vol. 41 Issue (4): 406-418    DOI:
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一类张量特征值互补问题
罗刚1, 杨庆之1,2
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
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摘要 矩阵特征值互补问题在力学系统领域有广泛的应用.在本文中,我们提出了一类特殊的四阶张量特征值互补问题,它是矩阵特征值互补问题的推广.我们对该特征值互补问题解的存在性,计算复杂度等性质进行了初步的研究.在一定条件下,我们建立了该互补问题同一类非线性约束优化问题的等价性联系,并由此提出了平移投影幂法来求解该特征值互补问题.
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关键词半正定锥   特征值互补问题   NP难   平移投影幂法     
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.
Key wordsPositive semidefinite cone   eigenvalue complementarity problem   N-P hardness   shifted power method   
收稿日期: 2018-03-28; 出版日期: 2019-11-16
基金资助:

国家自然科学基金项目(11671217),新疆自然科学基金项目(2017D01A14).

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.
 
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