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Journal of Global Optimization

, Volume 73, Issue 1, pp 223–237 | Cite as

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

  • Vu Trung HieuEmail author
Article

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.

Keywords

Monotone affine vector variational inequality Solution set Number of connected components Scalarization formula Skew-symmetric matrix 

Mathematics Subject Classification

49J40 47H05 90C29 90C33 

Notes

Acknowledgements

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

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Division of MathematicsPhuong Dong UniversityHanoiVietnam

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