On the Numbers of Connected Components in the Solution Sets of Polynomial Vector Variational Inequalities

  • Vu Trung HieuEmail author
Technical Notes


In this paper, we establish explicit upper bounds for the number of connected components in the proper Pareto solution sets and the weak Pareto solution sets of polynomial vector variational inequalities. Consequently, upper bounds for the numbers of connected components in the stationary point sets, the proper stationary point sets, and the weak Pareto solution sets of polynomial vector optimization problems are obtained.


Polynomial vector variational inequality Polynomial vector optimization Solution set Semi-algebraic set Number of connected components 

Mathematics Subject Classification

90C29 90C33 49J40 14P10 



The author is indebted to Professor Nguyen Dong Yen for many stimulating conversations. The author would like to thank the referees for their valuable comments which helped to improve the manuscript.


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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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