Second-order necessary and sufficient optimality conditions for multiobjective interval-valued nonlinear programming

Abstract

In this article, the second-order optimality conditions for nonlinear programming with multiple interval-valued objective functions (in brief, NPMIOF) are studied. In the first part, the second- and first-order necessary optimality conditions for some types of efficient solutions of NPMIOF are established under of Abadie second- and first-order constraint qualifications. In the next part, we investigate both primal and dual second-order sufficient optimality conditions. Our second-order necessary conditions enhance the previous results. The second-order sufficient optimality conditions are new.

Keywords:

• Multiobjective nonlinear programming
• interval-valued objective functions
• second-order necessary and sufficient optimality conditions
• second-order Abadie constraint qualifications

2020 Mathematics Subject Classifications:

• 90C46
• 90C29
• 90C70
• 90C30

Acknowledgements

The author would like to thank the editors for the help in the processing of the article. The author is very grateful to the anonymous referee for the valuable remarks, which helped to improve the paper.

Disclosure statement

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

Additional information

Funding

This work was supported by The Ministry of Education and Training of Vietnam[B2022-TCT-01].