Connectedness structure of the solution sets of vector variational inequalities. (3rd June 2017)

• Record Type: Journal Article
• Authors: Huong, N. T. T.; Yao, J.-C.; Yen, N. D.
• Is Part Of: Optimization. Volume 66:Number 6(2017)
• Page Start: 889
• Page End: 901
• Publication Date: 2017-06-03
• Subjects: Vector variational inequality -- solution set -- scalarization -- semi-algebraic set -- connectedness structure; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1172073
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : By a scalarization method and properties of semi-algebraic sets, it is proved that both the Pareto solution set and the weak Pareto solution set of a vector variational inequality, where the constraint set is polyhedral convex and the basic operators are given by polynomial functions, have finitely many connected components. Consequences of the results for vector optimization problems are discussed in details. The results of this paper solve in the affirmative some open questions for the case of general problems without requiring monotonicity of the operators involved.