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

Hai-Ying Wang (), Zu-Feng Fu () and Shi-Liang Wu ()
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Hai-Ying Wang: Nanyang Normal University
Zu-Feng Fu: Nanyang Normal University
Shi-Liang Wu: Yunnan Normal University

Journal of Optimization Theory and Applications, 2025, vol. 204, issue 1, No 2, 21 pages

Abstract: 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.

Keywords: Vertical tensor complementarity problem; Bound of the solution set; $$VR_{0}$$ V R 0 -tensor set; VP-tensor set; 90C33; 90C30; 65H10 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-024-02559-3

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