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On the Bound of the Solution Set for the Vertical Tensor Complementarity Problem

Author

Listed:
  • Hai-Ying Wang

    (Nanyang Normal University)

  • Zu-Feng Fu

    (Nanyang Normal University)

  • Shi-Liang Wu

    (Yunnan Normal University)

Abstract

This paper focuses on analyzing the boundness of the solution set for the vertical tensor complementarity problem (VTCP). We introduce two novel quantities related to tensor sets, establish the interconnections between these introduced quantities, and present an equivalent condition regarding a $$VR_{0}$$ V R 0 -tensor set based on a newly defined quantity. Additionally, we establish upper bounds for these quantities. We obtain several lower bounds of the solution set for the VTCP with a $$VR_{0}$$ V R 0 -tensor set. Leveraging the introduced quantities, we obtain several upper bounds of the solution set for the VTCP with a VP-tensor set or a $$VR_{0}$$ V R 0 -tensor set.

Suggested Citation

  • Hai-Ying Wang & Zu-Feng Fu & Shi-Liang Wu, 2025. "On the Bound of the Solution Set for the Vertical Tensor Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 204(1), pages 1-21, January.
    • Handle: RePEc:spr:joptap:v:204:y:2025:i:1:d:10.1007_s10957-024-02559-3
    DOI: 10.1007/s10957-024-02559-3
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    References listed on IDEAS

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    1. Yisheng Song & Wei Mei, 2018. "Structural Properties of Tensors and Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 176(2), pages 289-305, February.
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