Disconnectedness and unboundedness of the solution sets of monotone vector variational inequalities. Issue 3 (17th February 2021)

• Record Type: Journal Article
• Authors: Hieu, Vu Trung
• Is Part Of: Applicable analysis. Volume 100:Issue 3(2021)
• Page Start: 482
• Page End: 492
• Publication Date: 2021-02-17
• Subjects: Monotone vector variational inequality -- solution set -- disconnectedness -- unboundedness -- scalarization formula; 49J40 -- 47H05 -- 90C29 -- 90C33 -- 54D05; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1608962
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper, we investigate the topological structure of solution sets of monotone vector variational inequalities (VVIs). We show that if the weak Pareto solution set of a monotone VVI is disconnected, then each connected component of the set is unbounded. Similarly, this property holds for the proper Pareto solution set. Two open questions on the topological structure of the solution sets of (symmetric) monotone VVIs are raised at the end of the paper.