Properties of Structured Tensors and Complementarity Problems

Wei Mei () and Qingzhi Yang ()
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Wei Mei: Nankai University
Qingzhi Yang: Nankai University

Journal of Optimization Theory and Applications, 2020, vol. 185, issue 1, No 7, 99-114

Abstract: Abstract In this paper, we present some new results on a class of tensors, which are defined by the solvability of the corresponding tensor complementarity problem. For such structured tensors, we give a sufficient condition to guarantee the nonzero solution of the corresponding tensor complementarity problem with a vector containing at least two nonzero components and discuss their relationships with some other structured tensors. Furthermore, with respect to the tensor complementarity problem with a nonnegative such structured tensor, we obtain the upper and lower bounds of its solution set, and by the way, we show that the eigenvalues of such a tensor are closely related to this solution set.

Keywords: Structured tensor; Tensor complementarity problems; Strictly semi-positive tensor; Norm; Upper and lower bounds; 47H15; 47H12; 34B10; 47A52; 47J10; 47H09; 15A48; 47H07 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-020-01631-y

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