Robust optimality conditions and duality for nonsmooth multiobjective fractional semi-infinite programming problems with uncertain data

Abstract

In this article, some Karush-Kuhn-Tucker type robust optimality conditions and duality for an uncertain nonsmooth multiobjective fractional semi-infinite programming problem ((UMFP), for short) are established. First, we provide, by combining robust optimization and the robust limiting constraint qualification, robust necessary optimality conditions in terms of Mordukhovich's subdifferentials. Under suitable assumptions on the generalized convexity/the strictly generalized convexity, robust necessary optimality condition becomes robust sufficient optimality condition. Second, we formulate types of Mond-Weir and Wolfe robust dual problem for (UMFP) via the Mordukhovich subdifferentials. Finally, as an application, we establish weak/strong/converse robust duality theorems for the problem (UMFP) and its Mond-Weir and Wolfe types dual problem. Some illustrative examples are also provided for our findings.

Keywords:

• Nonsmooth multiobjective fractional semi-infinite programming problem with uncertain data
• robust (weakly) efficient solutions
• Karush-Kuhn-Tucker type robust optimality conditions
• Mordukhovich's subdifferentials

AMS CLASSIFICATIONs:

• 90C46
• 90C29
• 49K27
• 49J52

Acknowledgments

The authors are grateful to the anonymous referees and the associate editor for their valuable comments and suggestions, which helped to improve the quality of the paper in its present form.

Disclosure statement

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

Additional information

Funding

The first author was supported by the Science and Technology Fund of the Vietnam Ministry of Education and Training (B2022-BKA-02).