On the cone eigenvalue complementarity problem for higher-order tensors

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• 作者：Chen Ling ; Hongjin He ; Liqun Qi
• 关键词：Higher order tensor ; Eigenvalue complementarity problem ; Cone eigenvalue ; Optimization reformulation ; Projection algorithm
• 刊名：Computational Optimization and Applications
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：63
• 期：1
• 页码：143-168
• 全文大小：590 KB
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• 作者单位：Chen Ling (1)
  Hongjin He (1)
  Liqun Qi (2)
  
  1. Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, 310018, China
  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Optimization
  Operations Research and Mathematical Programming
  Operation Research and Decision Theory
  Statistics
  Convex and Discrete Geometry
  
• 出版者：Springer Netherlands
• ISSN：1573-2894

文摘

In this paper, we consider the tensor generalized eigenvalue complementarity problem (TGEiCP), which is an interesting generalization of matrix eigenvalue complementarity problem (EiCP). First, we give an affirmative result showing that TGEiCP is solvable and has at least one solution under some reasonable assumptions. Then, we introduce two optimization reformulations of TGEiCP, thereby beneficially establishing an upper bound on cone eigenvalues of tensors. Moreover, some new results concerning the bounds on the number of eigenvalues of TGEiCP further enrich the theory of TGEiCP. Last but not least, an implementable projection algorithm for solving TGEiCP is also developed for the problem under consideration. As an illustration of our theoretical results, preliminary computational results are reported.