Strong second-order Karush–Kuhn–Tucker optimality conditions for vector optimization

ABSTRACT

In the present paper, we focus on the vector optimization problems with inequality constraints, where objective functions and constrained functions are vector-valued functions with $C^{1,1}$ components defined on ${\mathbb{R}}^n$. By using the second-order symmetric subdifferential and the second-order tangent set, we propose two types of second-order regularity conditions in the sense of Abadie. Then we establish some strong second-order Karush–Kuhn–Tucker necessary optimality conditions for Geoffrion properly efficient solutions of the considered problem. Examples are given to illustrate the obtained results.

COMMUNICATED BY:

• Boris Mordukhovich

KEYWORDS:

• Symmetric second-order subdifferential
• Abadie second-order regularity condition
• Geoffrion properly efficient solution
• second-order Karush–Kuhn–Tucker optimality condition

AMS CLASSIFICATIONS:

• 49K30
• 49J52
• 49J53
• 90C29
• 90C46

Acknowledgements

The authors are indebted to the referee for valuable comments and suggestions which improved the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of Nguyen Van Tuyen was supported by the Ministry of Education and Training of Vietnam [grant number B2018-SP2-14]. The research of Do Sang Kim was supported by the National Research Foundation of Korea Grant funded by the Korean Government [NRF-2016R1A2B4011589].