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

2018/03/01 by Vu Trung Hieu, Hieu, Vu Trung
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1803.00201

openalex publication_date 2018/03/01 · openalex created_date 2020/02/14 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Existence of Pareto Solutions for Vector Polynomial Optimization Problems with Constraints
• Existence of Solutions and Relative Regularity Conditions for Polynomial Vector Optimization Problems
• Solution maps of polynomial variational inequalities
• Existence of Weak Pareto Efficient Solutions of a Vector Optimization Problem under a Closed Constraint Set
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