Global Uniqueness and Solvability of Tensor Variational Inequalities

Yong Wang, Zheng Hai Huang, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

39 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)137-152
Number of pages16
JournalJournal of Optimization Theory and Applications
Issue number1
Publication statusPublished - 1 Apr 2018


  • Exceptionally family of elements
  • Global uniqueness and solvability
  • Noncooperative game
  • Strictly positive definite tensor
  • Tensor variational inequality

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics


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