# Bilevel Optimization and Variational Analysis

## TL;DR

This chapter introduces a variational analysis framework for deriving necessary optimality conditions in bilevel optimization problems with Lipschitz data, focusing on optimistic models and discussing open problems.

## Contribution

It develops a self-contained variational analysis approach for bilevel optimization, extending to generalized differentiation and addressing optimistic models.

## Key findings

- Provides necessary optimality conditions for bilevel problems
- Applies variational analysis to Lipschitz data
- Discusses open problems in the field

## Abstract

This chapter presents a self-contained approach of variational analysis and generalized differentiation to deriving necessary optimality in problems of bilevel optimization with Lipschitzian data. We mainly concentrate on optimistic models, although the developed machinery also applies to pessimistic versions. Some open problems are posed and discussed.