Abstract
In this paper, some useful necessary and sufficient conditions for the unique solution of the generalized absolute value equation (GAVE) \(Ax-B|x|=b\) with \(A, B\in \mathbb {R}^{n\times n}\) from the optimization field are first presented, which cover the fundamental theorem for the unique solution of the linear system \(Ax=b\) with \(A\in \mathbb {R}^{n\times n}\). Not only that, some new sufficient conditions for the unique solution of the GAVE are obtained, which are weaker than the previous published works.
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Acknowledgements
The authors would like to thank the anonymous referees for providing helpful suggestions, which greatly improved the paper. This research was supported by National Natural Science Foundation of China (No. 11961082).
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Wu, S., Shen, S. On the unique solution of the generalized absolute value equation. Optim Lett 15, 2017–2024 (2021). https://doi.org/10.1007/s11590-020-01672-2
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DOI: https://doi.org/10.1007/s11590-020-01672-2