Some Properties of the Solution of the Extended Vertical Tensor Complementarity Problem

doi:10.1007/s40305-023-00531-y

Journal of the Operations Research Society of China ›› 2025, Vol. 13 ›› Issue (4): 946-965.doi: 10.1007/s40305-023-00531-y

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Some Properties of the Solution of the Extended Vertical Tensor Complementarity Problem

Li-Ming Li¹, Shi-Liang Wu^1,2, Cui-Xia Li¹

1 School of Mathematics, Yunnan Normal University, Kunming 650500, Yunnan, China;
2 Yunnan Key Laboratory of Modern Analytical Mathematics and Applications, Yunnan Normal University, Kunming 650500, Yunnan, China

Received:2023-04-14 Revised:2023-11-14 Online:2025-12-30 Published:2025-12-19
Contact: Shi-Liang Wu E-mail:slwuynnu@126.com
Supported by:
This research was supported by the National Natural Science Foundations of China (No. 11961082)

Abstract

Abstract: In this paper, we introduce the extended vertical tensor complementarity problem and investigate the existence and uniqueness of its solution. We introduce several sets of special tensors and demonstrate their properties. We leverage the structure of tensors to obtain some properties of the solution of the extended vertical tensor complementarity problem. Furthermore, we use degree theory and the equivalent form of the minimum function to establish sufficient conditions for the existence and uniqueness of the solution of the extended vertical tensor complementarity problem, respectively.

Key words: The extended vertical tensor complementarity problem, Special tensor sets, The degree theory, The minimum function

CLC Number:

Li-Ming Li, Shi-Liang Wu, Cui-Xia Li. Some Properties of the Solution of the Extended Vertical Tensor Complementarity Problem[J]. Journal of the Operations Research Society of China, 2025, 13(4): 946-965.

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References

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Some Properties of the Solution of the Extended Vertical Tensor Complementarity Problem

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