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Existence of the least element solution of the vertical block Z-tensor complementarity problem

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Abstract

The aim of this paper is to prove the existence of the least element solution to the vertical tensor complementarity problem when the involved tensor is a vertical block Z-tensor and the feasible set of the problem is nonempty. Our constructional proof shows that the least element solution of this problem can be found by solving a polynomial optimization problem. Two numerical examples are given to verify our findings.

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Acknowledgment

This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 12171357 and 11871051).

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  1. School of Mathematics, Tianjin University, Tianjin, 300350, People’s Republic of China

    Ruoke Meng, Zheng-Hai Huang & Yong Wang

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  1. Ruoke Meng
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  2. Zheng-Hai Huang
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Correspondence to Zheng-Hai Huang.

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Meng, R., Huang, ZH. & Wang, Y. Existence of the least element solution of the vertical block Z-tensor complementarity problem. Optim Lett 17, 1697–1709 (2023). https://doi.org/10.1007/s11590-023-01977-y

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