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Notes on the Optimization Problems Corresponding to Polynomial Complementarity Problems

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Abstract

This work is motivated by a conjecture of Che et al. (J Optim Theory Appl 168:475–487, 2016) which says that if the feasible region of a tensor complementarity problem is nonempty, then the corresponding optimization problem has a solution. The aim of the paper is twofold. First, we show several sufficient conditions for the solution existence of the optimization problems corresponding to polynomial complementarity problems. Consequently, some results for tensor complementarity problems are obtained. Second, we disprove the conjecture by giving a counterexample.

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Acknowledgements

The authors are grateful to the editor-in-chief and the anonymous referees for their valuable suggestions. The first author wishes to thank the Department of Applied Mathematics, National Sun Yat-Sen University and the Center for General Education, China Medical University for hospitality and support. The research of Yimin Wei is supported by the National Natural Science Foundation of China under Grant 11771099 and the Innovation Program of Shanghai Municipal Education Committee.

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Authors and Affiliations

  1. Division of Mathematics, Phuong Dong University, Hanoi, Vietnam

    Vu Trung Hieu

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

    Yimin Wei

  3. Center for General Education, China Medical University, Taichung, Taiwan

    Jen-Chih Yao

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  1. Vu Trung Hieu
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  2. Yimin Wei
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  3. Jen-Chih Yao
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Correspondence to Vu Trung Hieu.

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Communicated by Liqun Qi.

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Hieu, V.T., Wei, Y. & Yao, JC. Notes on the Optimization Problems Corresponding to Polynomial Complementarity Problems. J Optim Theory Appl 184, 687–695 (2020). https://doi.org/10.1007/s10957-019-01596-7

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  • DOI: https://doi.org/10.1007/s10957-019-01596-7

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