# Constraint qualifications and optimality conditions in bilevel optimization

arXiv: https://arxiv.org/abs/1910.04072 · HTML: https://mlsanity.com/paper/1910.04072/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Oct 2019.

## Built on by (most cited first, 5 of 5)

- [Investigating Bi-Level Optimization for Learning and Vision from a Unified Perspective: A Survey and Beyond](https://mlsanity.com/paper/2101.11517/) (2021)
- [First-order penalty methods for bilevel optimization](https://mlsanity.com/paper/2301.01716/) (2023)
- [Moreau Envelope Based Difference-of-weakly-Convex Reformulation and Algorithm for Bilevel Programs](https://mlsanity.com/paper/2306.16761/) (2023)
- [A Generalized Alternating Method for Bilevel Learning under the Polyak-Lojasiewicz Condition](https://mlsanity.com/paper/2306.02422/) (2023)
- [Solving bilevel optimization via sequential minimax optimization](https://mlsanity.com/paper/2511.07398/) (2025)

## Abstract (arXiv)

In this paper we study constraint qualifications and optimality conditions for bilevel programming problems. We strive to derive checkable constraint qualifications in terms of problem data and applicable optimality conditions. For the bilevel program with convex lower level program we discuss drawbacks of reformulating a bilevel programming problem by the mathematical program with complementarity constraints and present a new sharp necessary optimality condition for the reformulation by the mathematical program with a generalized equation constraint. For the bilevel program with a nonconvex lower level program we propose a relaxed constant positive linear dependence (RCPLD) condition for the combined program.