Estimates for coderivative of solution map in bilevel program

Abstract

This paper deals with a kind of nonconvex optimistic bilevel optimization programs. In some process of dealing this kind of bilevel programs, difficulties are essentially moved to estimating for coderivative of the solution map. To deal with these difficulties, we use value function of the lower level problem and its modifications as implicit functions to describe the solution map. By applying techniques in variational analysis, we give estimates for coderivative of the solution map. Then, we will show the applications in optimality conditions for these bilevel programs which we derived by using the extremal principle.

Keywords:

• Bilevel optimization
• coderivative
• set-valued optimization
• variational analysis
• optimality condition

AMS CLASSIFICATIONS:

• 90C26
• 90C46
• 49J52
• 49J53

Acknowledgements

The author is grateful to professor Lixin Cheng, for his kind and patient guidances on research and writing. The author thanks professor Qinjin Cheng, professor Wen Zhang and all students in the Functional Analysis group in Xiamen University for their valuable suggestions. Also, the author would like to thank professor Boris Mordukhovich for his kind and valuable comments and suggestions during this research. Also, the author wants to express his thanks to editors and referees for their valuable suggestions and comments on this paper.

Disclosure statement

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

Additional information

Funding

The work was supported by National Natural Science Foundation of China, grant No. 11731010,12071388.