Solvability of a regular polynomial vector optimization problem without convexity

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