Tensor Complementarity Problems—Part I: Basic Theory

Zheng Hai Huang, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

24 Citations (Scopus)

Abstract

Tensors (hypermatrices) are multidimensional analogs of matrices. The tensor complementarity problem is a class of nonlinear complementarity problems with the involved function being defined by a tensor, which is also a direct and natural extension of the linear complementarity problem. In the last few years, the tensor complementarity problem has attracted a lot of attention, and has been studied extensively, from theory to solution methods and applications. This work, with its three parts, aims at contributing to review the state-of-the-art of studies for the tensor complementarity problem and related models. In this part, we describe the theoretical developments for the tensor complementarity problem and related models, including the nonemptiness and compactness of the solution set, global uniqueness and solvability, error bound theory, stability and continuity analysis, and so on. The developments of solution methods and applications for the tensor complementarity problem are given in the second part and the third part, respectively. Some further issues are proposed in all the parts.

Original languageEnglish
JournalJournal of Optimization Theory and Applications
Volume183
Issue number1
DOIs
Publication statusPublished - 15 Oct 2019

Keywords

  • Error bound theory
  • Global uniqueness and solvability
  • Nonemptiness and compactness of the solution set
  • Stability and continuity analysis
  • Tensor complementarity problem

ASJC Scopus subject areas

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

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