Disciplined Bilevel Programming
Abstract
Bilevel optimization provides a natural modeling language for hierarchical decision problems. However, applying existing numerical solvers usually requires substantial manual analysis and reformulation. In this paper, we introduce disciplined bilevel programming (DBLP), a symbolic framework that allows users to specify and solve optimistic bilevel problems in a high-level, human-readable way that is close to the mathematical formulation. For problems with a disciplined nonlinear upper problem and a convex lower problem satisfying the disciplined parameterized programming rules, DBLP automatically canonicalizes the lower problem into conic form and constructs an equivalent single-level reformulation using the conic Karush-Kuhn-Tucker conditions. We relax the resulting complementarity constraint and use a gap continuation procedure to approximately solve a sequence of smooth nonlinear problems. We implement DBLP in the open-source Python package BLVPY, an extension of CVXPY for bilevel programming. We demonstrate the modeling and solution capabilities of BLVPY on a range of bilevel optimization problems from several application domains. The proposed framework and implementation allow users to specify and solve bilevel optimization problems within a few lines of code, without prior expertise in bilevel modeling and numerical optimization.
Related
- Necessary Optimality Conditions for Bilevel Programming using Tangential Subdifferentials
- Decision-focused predictions via pessimistic bilevel optimization: complexity and algorithms
- Stochastic Nonconvex Bilevel Optimization: Improved Rates Without Rare-Visit Assumption
- Linear-Time Bilevel Clipping operators for Structured Sparsity in Neural Networks
- Observability as a constraint qualification for a nonsmooth bilevel PDE-constrained problem
BibTeX
@misc{zhu2026disciplined,
title = {{Disciplined Bilevel Programming}},
author = {Hao Zhu and Joschka Boedecker},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.00644},
eprint = {2609.00644},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00644},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Disciplined Bilevel Programming
AU - Hao Zhu
AU - Joschka Boedecker
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2609.00644
UR - https://arxiv.org/abs/2609.00644
AB - Bilevel optimization provides a natural modeling language for hierarchical decision problems. However, applying existing numerical solvers usually requires substantial manual analysis and reformulation. In this paper, we introduce disciplined bilevel programming (DBLP), a symbolic framework that allows users to specify and solve optimistic bilevel problems in a high-level, human-readable way that is close to the mathematical formulation. For problems with a disciplined nonlinear upper problem and a convex lower problem satisfying the disciplined parameterized programming rules, DBLP automatically canonicalizes the lower problem into conic form and constructs an equivalent single-level reformulation using the conic Karush-Kuhn-Tucker conditions. We relax the resulting complementarity constraint and use a gap continuation procedure to approximately solve a sequence of smooth nonlinear problems. We implement DBLP in the open-source Python package BLVPY, an extension of CVXPY for bilevel programming. We demonstrate the modeling and solution capabilities of BLVPY on a range of bilevel optimization problems from several application domains. The proposed framework and implementation allow users to specify and solve bilevel optimization problems within a few lines of code, without prior expertise in bilevel modeling and numerical optimization.
ER -