  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.

Optimization and Control;Algebraic Geometry