Global Uniqueness and Solvability of Tensor Variational Inequalities

Yong Wang (), Zheng-Hai Huang () and Liqun Qi ()
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Yong Wang: Tianjin University
Zheng-Hai Huang: Tianjin University
Liqun Qi: The Hong Kong Polytechnic University

Journal of Optimization Theory and Applications, 2018, vol. 177, issue 1, No 7, 137-152

Abstract: 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.

Keywords: Tensor variational inequality; Global uniqueness and solvability; Noncooperative game; Strictly positive definite tensor; Exceptionally family of elements; 90C33; 90C30; 65H10 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (15)

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DOI: 10.1007/s10957-018-1233-5

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