# Optimality Conditions for Bilevel Programming: An Approach Through Variational Analysis

## Abstract

In this article, we focus on the study of bilevel programming problems where the feasible set in the lower-level problem is an abstract closed convex set and not described by any equalities and inequalities. In such a situation, we can view them as MPEC problems and develop necessary optimality conditions. We also relate various solution concepts in bilevel programming and establish some new connections. We study in considerable detail the notion of partial calmness and its application to derive necessary optimality conditions and also give some illustrative examples.

## Notes

### Acknowledgements

I am grateful to the organizers of the CIMPA school on Generalized Nash Equilibrium, Bilevel Programming and MPEC problems held in Delhi from 25 November to 6 December 2013 for giving me a chance to speak at the workshop which finally led to this article. I would also like to thank Didier Aussel for his thoughtful discussions on the article and his help in constructing Example 3.3. I am also indebted to the anonymous referee for the constructive suggestion which improved the presentation of this article.

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