  In this paper we consider the solvability of a non-convex regular polynomial
vector optimization problem on a nonempty closed set. We introduce regularity
conditions for the polynomial vector optimization problem and study properties
and characterizations of the regularity conditions. Under the regularity
conditions, we study nonemptiness and boundedness of the solution sets of the
problem. As a consequence, we establish two Frank-Wolfe type theorems for the
non-convex polynomial vector optimization problem. Finally, we investigate the
solution stability of the non-convex regular polynomial vector optimization
problem.
