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Minimax Theory and its Applications 05 (2020), No. 1, 019--031
Copyright Heldermann Verlag 2020

An Application of the Tarski-Seidenberg Theorem with Quantifiers to Vector Variational Inequalities

Vu Trung Hieu
Division of Mathematics, Phuong Dong University, Cau Giay, Hanoi, Vietnam

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 Tarski-Seidenberg Theorem with quantifiers, we are able to prove that these solution sets are semi-algebraic without imposing the Mangasarian-Fromovitz constraint qualification on the system of constraints.

Keywords: Polynomial vector variational inequality, polynomial vector optimization, solution set, connectedness structure, semi-algebraic set.

MSC: 14P10, 49J40, 90C29, 90C33.

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