Solvability of a regular polynomial vector optimization problem without convexity

ABSTRACT

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.

KEYWORDS:

• Polynomial vector optimization problem
• regularity condition
• Frank–Wolfe type theorem
• non-convexity
• stability

2020 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 90C29
• 90C23
• 49K40

Acknowledgements

The authors would like to thank the referees and the handling editor for their helpful comments and suggestions, which have led to the improvement of the earlier version of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China [grant number 11471230].