Year: 2017
Type: preprint
Abstract: In this paper, we introduce 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; and we call it the tensor variational inequality (TVI). The TVI 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 TVI. In particular, we investigate the global uniqueness and solvability of the TVI. To this end, we first introduce two classes of structured tensors and discuss some related properties; and then, we show that the TVI has the property of global uniqueness and solvability under some assumptions, which is different from the existed result for the general variational inequality.
Source: arXiv (Cornell University)
Authors: Wang, Yong, Huang, Zheng-Hai, Qi, Liqun
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2582173221