Robust duality for nonconvex uncertain vector optimization via a general scalarization

ABSTRACT

This paper concentrates on robust duality relations for uncertain cone-constrained vector optimization problems in more general nonconvex settings. First, different from the existing results, a new class of generalized Lagrange functions of the considered problem is introduced by combining the image space analysis method and scalarization technique. Then, the Lagrange robust vector dual problem is formulated. Subsequently, the results of robust weak duality, strong duality and converse duality are given respectively, which characterize vector dual relations between the primal worst and dual best problems. Simultaneously, some examples are given to illustrate our results.

KEYWORDS:

• Robust duality
• uncertain vector optimizations
• scalarization
• nonconvexity
• image space analysis

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 90C46
• 90C29
• 90C31

Acknowledgments

The authors are grateful to the editor and two anonymous referees for their valuable comments and suggestions, which improved the quality of the paper.

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 China [grant number 11971078].