Numbers of the connected components of the solution sets of monotone affine vector variational inequalities
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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.
KeywordsMonotone affine vector variational inequality Solution set Number of connected components Scalarization formula Skew-symmetric matrix
Mathematics Subject Classification49J40 47H05 90C29 90C33
The author is indebted to Professor Nguyen Dong Yen for many stimulating conversations.
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