Global Uniqueness and Solvability for Tensor Complementarity Problems

Xue-Li Bai, Zheng-Hai Huang () and Yong Wang
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Xue-Li Bai: Tianjin University
Zheng-Hai Huang: Tianjin University
Yong Wang: Tianjin University

Journal of Optimization Theory and Applications, 2016, vol. 170, issue 1, No 5, 72-84

Abstract: Abstract Recently, the tensor complementarity problem has been investigated in the literature. An important question involving the property of global uniqueness and solvability for a class of tensor complementarity problems was proposed by Song and Qi (J Optim Theory Appl, 165:854–873, 2015). In the present paper, we give an answer to this question by constructing two counterexamples. We also show that the solution set of this class of tensor complementarity problems is nonempty and compact. In particular, we introduce a class of related structured tensors and show that the corresponding tensor complementarity problem has the property of global uniqueness and solvability.

Keywords: Tensor complementarity problem; Nonlinear complementarity problem; Global uniqueness and solvability; P tensor; Strong P tensor; 90C33; 65K10; 15A18; 15A69; 65F15; 65F10 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (37)

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DOI: 10.1007/s10957-016-0903-4

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