# On Stability in Optimistic Bilevel Optimization

arXiv: https://arxiv.org/abs/2408.13323 · HTML: https://mlsanity.com/paper/2408.13323/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 50 references that are in the map.
- First posted on arXiv 23 Aug 2024.

## Builds on (most cited first, 9 of 9)

- [A Fully First-Order Method for Stochastic Bilevel Optimization](https://mlsanity.com/paper/2301.10945/) (2023)
- [On Penalty Methods for Nonconvex Bilevel Optimization and First-Order Stochastic Approximation](https://mlsanity.com/paper/2309.01753/) (2023)
- [Optimal Algorithms for Stochastic Bilevel Optimization under Relaxed Smoothness Conditions](https://mlsanity.com/paper/2306.12067/) (2023)
- [Value-Function-based Sequential Minimization for Bi-level Optimization](https://mlsanity.com/paper/2110.04974/) (2021)
- [A Unified Framework for Multistage and Multilevel Mixed Integer Linear Optimization](https://mlsanity.com/paper/2104.09003/) (2021)
- [New characterizations of Hoffman constants for systems of linear constraints](https://mlsanity.com/paper/1905.02894/) (2019)
- [On a Computationally Ill-Behaved Bilevel Problem with a Continuous and Nonconvex Lower Level](https://mlsanity.com/paper/2202.01033/) (2022)
- [Two-level value function approach to nonsmooth optimistic and pessimistic bilevel programs](https://mlsanity.com/paper/1711.11127/) (2017)
- [A Framework for Generalized Benders' Decomposition and Its Application to Multilevel Optimization](https://mlsanity.com/paper/2104.06496/) (2021)

## Abstract (arXiv)

Solutions of bilevel optimization problems tend to suffer from instability under changes to problem data. In the optimistic setting, we construct a lifted formulation that exhibits desirable stability properties under mild assumptions that neither invoke convexity nor smoothness. The upper- and lower-level problems might involve integer restrictions and disjunctive constraints. In a range of results, we invoke at most pointwise and local calmness for the lower-level problem in a sense that holds broadly. The lifted formulation is computationally attractive with structural properties being brought out and an outer approximation algorithm becoming available.