Robust nonsmooth optimality conditions for multiobjective optimization problems with infinitely many uncertain constraints

Abstract

This paper concentrates on uncertain multiobjective optimization problems with an arbitrary number of uncertain constraints under nonconvex and nonsmooth assumptions. We analyse the properties of robust infinite constraints and arrive at the Clarke subdifferential of the double supremum function. Subsequently, we employ the obtained subdifferential rules to study KKT robust necessary and sufficient optimality conditions for two types of uncertain multiobjective optimization problems. Simultaneously, some illustrative examples are provided to show the validity of the main results. Our results are new and generalize several corresponding results in the literature.

Keywords:

• KKT robust optimality conditions
• uncertain multiple objectives
• multiple interval-valued objectives
• robust infinite constraints

2010 Mathematics Subject Classifications:

• 90C46
• 90C29
• 49K10
• 62G35

Acknowledgments

The authors are grateful to the editor and two anonymous referees for their constructive 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 numbers 11971078 and 11571055], the Fundamental Research Funds for the Central Universities [grant number 106112017CDJZRPY0020].