
Minimax Theory and its Applications 05 (2020), No. 1, 019031 Copyright Heldermann Verlag 2020 An Application of the TarskiSeidenberg Theorem with Quantifiers to Vector Variational Inequalities Vu Trung Hieu Division of Mathematics, Phuong Dong University, Cau Giay, Hanoi, Vietnam hieuvut@gmail.com We study the connectedness structure of the proper Pareto solution sets, the Pareto solution sets, the weak Pareto solution sets of polynomial vector variational inequalities, as well as the connectedness structure of the efficient solution sets and the weakly efficient solution sets of polynomial vector optimization problems. By using the TarskiSeidenberg Theorem with quantifiers, we are able to prove that these solution sets are semialgebraic without imposing the MangasarianFromovitz constraint qualification on the system of constraints. Keywords: Polynomial vector variational inequality, polynomial vector optimization, solution set, connectedness structure, semialgebraic set. MSC: 14P10, 49J40, 90C29, 90C33. [ Fulltextpdf (118 KB)] for subscribers only. 