Necessary optimality conditions for nonsmooth robust optimization problems

ABSTRACT

In this paper, we investigate robust necessary optimality for scalar uncertain optimization problems under the strictly robust counterpart, where the uncertainties are included in the objective and the constraints. Based on generalized differentiable assumptions, some robust necessary conditions via a separation scheme are derived. Besides, by means of strong separation functions, several characterizations of robust necessary optimality can be established. Finally, an example is given to show the effectiveness of the results derived in this paper.

Keywords:

• Image space analysis
• scalar robust optimization
• robust optimality condition
• separation

Mathematics Subject Classifications 2010:

• 90C31
• 90C30
• 90C46

Acknowledgments

The authors gratefully thank the associate editor and anonymous referees for their constructive suggestions and comments, which have helped to improve 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 12001348, 11971078], the Project funded by China Postdoctoral Science Foundation [grant number 2019M660247] and the Fundamental Research Funds for the Central Universities [grant numbers GK202003010, 106112017CDJZRPY0020].