张量空间上的仿射变分不等式  

Affine variational inequalities over tensor spaces

作　　者：李夏 黄正海 Xia Li;Zhenghai Huang

机构地区：[1]天津大学数学学院,天津300350

出　　处：《中国科学：数学》2022年第3期355-368,共14页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11871051)资助项目。

摘　　要：本文考虑张量空间上的变分不等式并讨论一些基本性质.特别地,借助一类张量乘积,定义一类张量空间上的仿射变分不等式,讨论这类变分不等式解集的性质,包括解的存在唯一性和解集的有界性.最后考察一类寡头垄断市场博弈问题,将其建模为一个张量空间上的仿射变分不等式,为此类问题的进一步研究提供动力.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 solution set of the affine variational inequality,including existence and uniqueness of the solution and boundedness of the solution 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.

关 键 词：仿射变分不等式 张量空间 张量积 寡头垄断市场博弈 

分 类 号：O178[理学—数学]