Numbers of the connected components of the solution sets of monotone affine vector variational inequalities
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 [N.D. Yen and J.C. Yao, \textit{Monotone affine vector variational inequalities}, Optimization 60 (2011), pp. 5368] 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2018
 arXiv:
 arXiv:1803.00198
 Bibcode:
 2018arXiv180300198H
 Keywords:

 Mathematics  Optimization and Control;
 Mathematics  General Topology;
 49J40;
 47H05;
 90C29;
 90C33
 EPrint:
 17 pages