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Positive-Definite Tensors to Nonlinear Complementarity Problems

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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.

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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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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, People’s Republic of China

    Maolin Che

  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong

    Liqun Qi

  3. School of Mathematical Sciences and Shanghai Key Laboratory of Contemporary Applied Mathematics, Fudan University, Shanghai, 200433, People’s Republic of China

    Yimin Wei

Authors
  1. Maolin Che
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  2. Liqun Qi
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  3. Yimin Wei
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Correspondence to Yimin Wei.

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Che, M., Qi, L. & Wei, Y. Positive-Definite Tensors to Nonlinear Complementarity Problems. J Optim Theory Appl 168, 475–487 (2016). https://doi.org/10.1007/s10957-015-0773-1

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  • DOI: https://doi.org/10.1007/s10957-015-0773-1

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