Structural Properties of Tensors and Complementarity Problems

Yisheng Song () and Wei Mei ()
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Yisheng Song: Henan Normal University
Wei Mei: Henan Normal University

Journal of Optimization Theory and Applications, 2018, vol. 176, issue 2, No 2, 289-305

Abstract: Abstract In this paper, one of our main purposes is to prove the boundedness of the solution set of tensor complementarity problems such that the specific bounds depend only on the structural properties of such a tensor. To achieve this purpose, firstly, we prove that this class of structured tensors is strictly semi-positive. Subsequently, the strictly lower and upper bounds of operator norms are given for two positively homogeneous operators. Finally, with the help of the above upper bounds, we show that the solution set of tensor complementarity problems has the strictly lower bound. Furthermore, the upper bounds of spectral radius are obtained, which depends only on the principal diagonal entries of tensors.

Keywords: Structured tensor; Tensor complementarity problems; Spectral radius; Operator norms; Upper and lower bounds; 47H15; 47H12; 34B10; 47A52; 47J10; 47H09; 15A48; 47H07 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s10957-017-1212-2

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