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Generalized Polynomial Complementarity Problems over a Polyhedral Cone

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Abstract

The goal of this paper is to investigate a new model, called generalized polynomial complementarity problems over a polyhedral cone and denoted by GPCPs, which is a natural extension of the polynomial complementarity problems and generalized tensor complementarity problems. Firstly, the properties of the set of all \(R^{K}_{{\varvec{0}}}\)-tensors are investigated. Then, the nonemptiness and compactness of the solution set of GPCPs are proved, when the involved tensor in the leading term of the polynomial is an \(ER^{K}\)-tensor. Subsequently, under fairly mild assumptions, lower bounds of solution set via an equivalent form are obtained. Finally, a local error bound of the considered problem is derived. The results presented in this paper generalize and improve the corresponding those in the recent literature.

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Acknowledgements

The authors are grateful to the Editor and the reviewers for their helpful comments and suggestions, which have improved the presentation of the paper. This work was partially supported by National Natural Science Foundation of China (No.11961006), Guangxi Natural Science Foundation (2020GXNSFAA159100), and Guangxi Science and Technology Project (GuiKe-AD18126010).

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Authors and Affiliations

  1. School of Mathematics and Physics, Guangxi University for Nationalities, Nanning, 530006, Guangxi, People’s Republic of China

    Tong-tong Shang, Jing Yang & Guo-ji Tang

  2. Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Nanning, 530006, Guangxi, People’s Republic of China

    Guo-ji Tang

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  1. Tong-tong Shang
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Correspondence to Guo-ji Tang.

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Communicated by Alexey F. Izmailov.

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Shang, Tt., Yang, J. & Tang, Gj. Generalized Polynomial Complementarity Problems over a Polyhedral Cone. J Optim Theory Appl 192, 443–483 (2022). https://doi.org/10.1007/s10957-021-01969-x

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