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Numbers of the connected components of the solution sets of monotone affine vector variational inequalities

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Abstract

This paper establishes several upper and lower estimates for the maximal number of the connected components of the solution sets of monotone affine vector variational inequalities. Our results give a partial solution to Question 2 in Yen and Yao (Optimization 60:53–68, 2011) and point out that the number depends not only on the number of the criteria but also on the number of variables of the vector variational inequality under investigation.

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Acknowledgements

The author is indebted to Professor Nguyen Dong Yen for many stimulating conversations.

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  1. Division of Mathematics, Phuong Dong University, 171 Trung Kinh Street, Cau Giay, Hanoi, Vietnam

    Vu Trung Hieu

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  1. Vu Trung Hieu
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Correspondence to Vu Trung Hieu.

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Hieu, V.T. Numbers of the connected components of the solution sets of monotone affine vector variational inequalities. J Glob Optim 73, 223–237 (2019). https://doi.org/10.1007/s10898-018-0678-2

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  • DOI: https://doi.org/10.1007/s10898-018-0678-2

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