mlsanityData to 14 Oct 2026

Unrolled Graph Neural Networks for Constrained Optimization

arXiv 2509.17156 ↗First posted 21 Sep 2025cs.LGcited by 1

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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.

Key facts. Cited by 1 paper 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

23 of 29 references.

References · 23

  1. 2021Convex optimizationcited by 2,515
  2. 2019Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processingcited by 421
  3. 2019Exact Combinatorial Optimization with Graph Convolutional Neural Networkscited by 318
  4. 2021Combinatorial optimization and reasoning with graph neural networkscited by 268
  5. 2020Deep Unfolding Network for Image Super-Resolutioncited by 254
  6. 2022Deep Generalized Unfolding Networks for Image Restorationcited by 121
  7. 2020Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networkscited by 75
  8. 2022Self-Supervised Primal-Dual Learning for Constrained Optimizationcited by 61
  9. 2021Constrained Learning with Non-Convex Lossescited by 42
  10. 2022On Representing Linear Programs by Graph Neural Networkscited by 39
  11. 2025RUN: Reversible Unfolding Network for Concealed Object Segmentationcited by 28
  12. 2024Real-world Image Dehazing with Coherence-based Pseudo Labeling and Cooperative Unfolding Networkcited by 26
11 more
  1. 2018Deep Unfolding of a Proximal Interior Point Method for Image Restorationcited by 24
  2. 2024PDHG-Unrolled Learning-to-Optimize Method for Large-Scale Linear Programmingcited by 17
  3. 2024Expressive Power of Graph Neural Networks for (Mixed-Integer) Quadratic Programscited by 16
  4. 2021Graph Signal Restoration Using Nested Deep Algorithm Unrollingcited by 13
  5. 2021Space-Time Graph Neural Networkscited by 10
  6. 2023Robust Stochastically-Descending Unrolled Networkscited by 9
  7. 2025Proximal Algorithm Unrolling: Flexible and Efficient Reconstruction Networks for Single-Pixel Imagingcited by 8
  8. 2022Deep Unfolding of the DBFB Algorithm with Application to ROI CT Imaging with Limited Angular Densitycited by 6
  9. 2023Stochastic Unrolled Federated Learningcited by 6
  10. 2022Space-Time Graph Neural Networks with Stochastic Graph Perturbationscited by 5
  11. 2023Deep Unrolling Networks with Recurrent Momentum Acceleration for Nonlinear Inverse Problemscited by 3

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026A Constrained Optimization Perspective of Unrolled Transformerscited by 0