# Continuous cutting plane algorithms in integer programming

arXiv: https://arxiv.org/abs/2204.09122 · HTML: https://mlsanity.com/paper/2204.09122/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Apr 2022.

## Built on by (most cited first, 4 of 4)

- [Towards graph neural networks for provably solving convex optimization problems](https://mlsanity.com/paper/2502.02446/) (2025)
- [Differentiable Cutting-plane Layers for Mixed-integer Linear Optimization](https://mlsanity.com/paper/2311.03350/) (2023)
- [Learn2Aggregate: Supervised Generation of Chv'atal-Gomory Cuts Using Graph Neural Networks](https://mlsanity.com/paper/2409.06559/) (2024)
- [The Differentiable Feasibility Pump](https://mlsanity.com/paper/2411.03535/) (2024)

## Abstract (arXiv)

Cutting planes for mixed-integer linear programs (MILPs) are typically computed in rounds by iteratively solving optimization problems, the so-called separation. Instead, we reframe the problem of finding good cutting planes as a continuous optimization problem over weights parametrizing families of valid inequalities. This problem can also be interpreted as optimizing a neural network to solve an optimization problem over subadditive functions, which we call the subadditive primal problem of the MILP. To do so, we propose a concrete two-step algorithm, and demonstrate empirical gains when optimizing generalized Gomory mixed-integer inequalities over various classes of MILPs. Code for reproducing the experiments can be found at https://github.com/dchetelat/subadditive.