Lagrange multiplier rules for weak approximate Pareto solutions to constrained vector optimization problems with variable ordering structures

ABSTRACT

In this paper, we consider the weak approximate solutions to constrained vector optimization problems with variable ordering structures. In terms of abstract subdifferentials, normal cones and coderivatives, we establish Lagrange rules for this kind of solutions.

Keywords:

• Vector optimization
• variable structure
• approximate solution
• abstract subdifferential

Mathematics Subject Classifications:

• 90C29
• 90C30
• 90C48
• 45J53

Acknowledgements

The authors are grateful to the associate editor and two anonymous reviewers for their extremely insightful, constructive, and detailed comments and suggestions, which improve the presentation of the paper. Moreover, the authors also appreciate the valuable comments given by Prof. Zheng.

Disclosure statement

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

Additional information

Funding

This research was supported by the National Natural Science Foundation of P.R. China [grant numbers 11771384 and 11801497] and  the Project for Young-notch Talents in the Ten Thousand Talent Program of Yunnan Province.