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Global Error Bound for the Vertical Tensor Complementarity Problem

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Abstract

As a natural extension of the tensor complementarity problem, the vertical tensor complementarity problem \(\left( {\textrm{VTCP}}\right) \) has important research value. In this paper, we get some properties of the solution of the VTCP. Furthermore, we focus on investigating the global error bound for the VTCP with the type \({\textrm{VP}}\) tensor set. We define two positively homogeneous operators by the type \({\textrm{VP}}\) tensor set and obtain two global error bounds of the VTCP through the positively homogeneous operators.

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Acknowledgements

The authors would like to thank both referees, whose opinions and comments improved the presentation of the paper greatly.

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Authors and Affiliations

  1. School of Mathematics, Yunnan Normal University, Kunming, 650500, Yunnan, People’s Republic of China

    Li-Ming Li & Shi-Liang Wu

  2. Yunnan Key Laboratory of Modern Analytical Mathematics and Applications, Yunnan Normal University, Kunming, 650500, Yunnan, People’s Republic of China

    Li-Ming Li & Shi-Liang Wu

  3. School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, 521041, Guangdong, People’s Republic of China

    Ping-Fan Dai

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  1. Li-Ming Li
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  2. Shi-Liang Wu
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Correspondence to Shi-Liang Wu.

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Communicated by Fabian Flores-Baz\(\grave{a }\)n.

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This research was supported by National Natural Science Foundations of China (No. 11961082).

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Li, LM., Wu, SL. & Dai, PF. Global Error Bound for the Vertical Tensor Complementarity Problem. J Optim Theory Appl 200, 1056–1077 (2024). https://doi.org/10.1007/s10957-023-02358-2

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  • DOI: https://doi.org/10.1007/s10957-023-02358-2

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