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Title: Global uniqueness and solvability of tensor variational inequalities
Authors: Wang, Y
Huang, ZH
Qi, L 
Keywords: Exceptionally family of elements
Global uniqueness and solvability
Noncooperative game
Strictly positive definite tensor
Tensor variational inequality
Issue Date: 2018
Publisher: Springer
Source: Journal of optimization theory and applications, 2018, v. 177, no. 1, p. 137-152 How to cite?
Journal: Journal of optimization theory and applications 
Abstract: In this paper, we consider a class of variational inequalities, where the involved function is the sum of an arbitrary given vector and a homogeneous polynomial defined by a tensor; we call it the tensor variational inequality. The tensor variational inequality is a natural extension of the affine variational inequality and the tensor complementarity problem. We show that a class of multi-person noncooperative games can be formulated as a tensor variational inequality. In particular, we investigate the global uniqueness and solvability of the tensor variational inequality. To this end, we first introduce two classes of structured tensors and discuss some related properties, and then, we show that the tensor variational inequality has the property of global uniqueness and solvability under some assumptions, which is different from the existing result for the general variational inequality.
ISSN: 0022-3239
EISSN: 1573-2878
DOI: 10.1007/s10957-018-1233-5
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