Affine variational inequalities over tensor spaces
Xia Li, Huang Zhenghai · Scientia Sinica Mathematica · 2020
In this paper, we consider variational inequalities over tensor spaces and discuss some basic properties. In particular, we introduce a type of product between two tensors, and with this tensor product, we define a class of affine variational inequalities over tensor spaces. Then, we discuss some properties of the 解 set of the affine variational inequality, including existence and uniqueness of the 解 and boundedness of the 解 set. Finally, we investigate a class of oligopolistic market games and transform it into an affine variational inequality over a tensor space, which provides important impetus for further study for this class of problems.