# Unrolled Graph Neural Networks for Constrained Optimization

arXiv: https://arxiv.org/abs/2509.17156 · HTML: https://mlsanity.com/paper/2509.17156/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 29 references that are in the map.
- First posted on arXiv 21 Sep 2025.

## Builds on (most cited first, 23 of 23)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Combinatorial optimization and reasoning with graph neural networks](https://mlsanity.com/paper/2102.09544/) (2021)
- [Deep Unfolding Network for Image Super-Resolution](https://mlsanity.com/paper/2003.10428/) (2020)
- [Deep Generalized Unfolding Networks for Image Restoration](https://mlsanity.com/paper/2204.13348/) (2022)
- [Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks](https://mlsanity.com/paper/2003.03777/) (2020)
- [Self-Supervised Primal-Dual Learning for Constrained Optimization](https://mlsanity.com/paper/2208.09046/) (2022)
- [Constrained Learning with Non-Convex Losses](https://mlsanity.com/paper/2103.05134/) (2021)
- [On Representing Linear Programs by Graph Neural Networks](https://mlsanity.com/paper/2209.12288/) (2022)
- [RUN: Reversible Unfolding Network for Concealed Object Segmentation](https://mlsanity.com/paper/2501.18783/) (2025)
- [Real-world Image Dehazing with Coherence-based Pseudo Labeling and Cooperative Unfolding Network](https://mlsanity.com/paper/2406.07966/) (2024)
- [Deep Unfolding of a Proximal Interior Point Method for Image Restoration](https://mlsanity.com/paper/1812.04276/) (2018)
- [PDHG-Unrolled Learning-to-Optimize Method for Large-Scale Linear Programming](https://mlsanity.com/paper/2406.01908/) (2024)
- [Expressive Power of Graph Neural Networks for (Mixed-Integer) Quadratic Programs](https://mlsanity.com/paper/2406.05938/) (2024)
- [Graph Signal Restoration Using Nested Deep Algorithm Unrolling](https://mlsanity.com/paper/2106.15910/) (2021)
- [Space-Time Graph Neural Networks](https://mlsanity.com/paper/2110.02880/) (2021)
- [Robust Stochastically-Descending Unrolled Networks](https://mlsanity.com/paper/2312.15788/) (2023)
- [Proximal Algorithm Unrolling: Flexible and Efficient Reconstruction Networks for Single-Pixel Imaging](https://mlsanity.com/paper/2505.23180/) (2025)
- [Deep Unfolding of the DBFB Algorithm with Application to ROI CT Imaging with Limited Angular Density](https://mlsanity.com/paper/2209.13264/) (2022)
- [Stochastic Unrolled Federated Learning](https://mlsanity.com/paper/2305.15371/) (2023)
- [Space-Time Graph Neural Networks with Stochastic Graph Perturbations](https://mlsanity.com/paper/2210.16270/) (2022)
- [Deep Unrolling Networks with Recurrent Momentum Acceleration for Nonlinear Inverse Problems](https://mlsanity.com/paper/2307.16120/) (2023)

## Built on by (most cited first, 1 of 1)

- [A Constrained Optimization Perspective of Unrolled Transformers](https://mlsanity.com/paper/2601.17257/) (2026)

## Abstract (arXiv)

In this paper, we unroll the dynamics of the dual ascent (DA) algorithm in two coupled graph neural networks (GNNs) to solve constrained optimization problems. The two networks interact with each other at the layer level to find a saddle point of the Lagrangian. The primal GNN finds a stationary point for a given dual multiplier, while the dual network iteratively refines its estimates to reach an optimal solution. We force the primal and dual networks to mirror the dynamics of the DA algorithm by imposing descent and ascent constraints. We propose a joint training scheme that alternates between updating the primal and dual networks. Our numerical experiments demonstrate that our approach yields near-optimal near-feasible solutions and generalizes well to out-of-distribution (OOD) problems.