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Journal of Optimization Theory and Applications

, Volume 168, Issue 2, pp 475–487 | Cite as

Positive-Definite Tensors to Nonlinear Complementarity Problems

  • Maolin Che
  • Liqun Qi
  • Yimin WeiEmail author
Article

Abstract

The main purpose of this paper was to investigate some kinds of nonlinear complementarity problems (NCP). For the structured tensors, such as symmetric positive-definite tensors and copositive tensors, we derive the existence theorems on a solution of these kinds of nonlinear complementarity problems. We prove that a unique solution of the NCP exists under the condition of diagonalizable tensors.

Keywords

Copositive tensor Symmetric tensor Positive-definite tensor Diagonalizable tensors Nonlinear complementarity problems 

Mathematics Subject Classification

15A18 15A69 65F15 65F10 

Notes

Acknowledgments

The authors would like to thank the anonymous referees for their valuable suggestions which help us to improve the manuscript. The first and the third authors are supported by the National Natural Science Foundation of China under Grant 11271084, and the second author was supported by the Hong Kong Research Grant Council (Grant Nos. PolyU 502510, 502111, 501212, 501913).

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.School of Mathematical SciencesFudan UniversityShanghaiPeople’s Republic of China
  2. 2.Department of Applied MathematicsThe Hong Kong Polytechnic UniversityKowloonHong Kong
  3. 3.School of Mathematical Sciences and Shanghai Key Laboratory of Contemporary Applied MathematicsFudan UniversityShanghaiPeople’s Republic of China

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