Necessary optimality conditions for strictly robust bilevel optimization problems

Abstract

The study of robust bilevel programming problems is a relatively new area of optimization theory. In this work, we investigate a bilevel optimization problem where the upper-level and the lower-level constraints incorporate uncertainty. Reducing the problem into a single-level nonlinear and nonsmooth program, necessary optimality conditions are then developed in terms of Clarke subdifferentials. Our approach consists of using the optimal value reformulation together with a partial calmness condition for the robust counterpart of the initial problem. To aid in the detection of Karush-Kuhn-Tucker (KKT) multipliers, an appropriate nonsmooth Mangasarian-Fromovitz constraint qualification is introduced. There are examples highlighting both our results and the limits of certain past studies.

Keywords:

• Bilevel optimization
• optimality conditions
• partial calmness
• robust optimization

2020 Mathematics Subject Classifications:

• 90C25
• 90C26
• 90C17
• 90C46

Acknowledgments

Our sincere acknowledgements to the anonymous referees for their insightful remarks and suggestions.

Disclosure statement

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