Learning SOCP Solver Dynamics with Graph Neural Networks

Abstract

Second-order cone programs (SOCPs) are a fundamental class of convex optimization problems widely applied across engineering domains. Classical interior-point methods are robust and accurate, but their iterative nature can be costly in real-time or repeated-solve settings. This has motivated learning-based solvers that approximate optimizer solutions with neural networks. Recent work has increasingly studied graph neural networks (GNNs) for linear, quadratic, and second-order cone optimization, leveraging their ability to model sparse relational structure among variables, constraints, and objective functions. Most existing GNN-based solvers compress the optimization process into a single forward pass, predicting the optimizer directly without using the intermediate trajectory produced by classical solvers. We introduce SOCPNet, a recursive GNN framework that uses solver trajectories to learn an iterative SOCP solution procedure. A shared GNN model is applied repeatedly, refining the current iterate at each step and enabling inference for a variable number of iterations. Rather than predicting the solution in a single pass, SOCPNet learns from intermediate iterates to progressively refine its estimates using a trajectory-regularized training procedure. We evaluate SOCPNet on multiple datasets spanning standard SOCP problem classes and show that it consistently reduces the final solution error relative to a SOCP-GNN baseline. Finally, we demonstrate how trained SOCPNet models can be used in a hybrid optimization pipeline by warm-starting a classical interior-point solver, reducing solver iterations without loss of accuracy.

Learning to Guide Ontology-Driven Geological Interpretation with Graph Neural Networks
Aya Attia, Gautier Laurent, Imadeddine Laouici
HAL4 Nov 2026PreprintCC BY-NC-ND 4.0Full textGeology & geochemistry StatisticsHAL
Learning Subgroup Relations Using Siamese Graph Neural Networks
Tal Weissblat
arXiv5 Sep 2026PreprintarXiv licenceFull textAlgebra & number theoryarXiv
Data-Driven On/Off Topology Optimization of Electromagnetic Devices Based on Graph Physics-Informed Neural Networks and Physics-Guided Reinforcement Learning
Xiaoyu Liu, Yihan Si, Wei Xiang +1
Mathematics9 Oct 2026Peer-reviewedCC BY 4.0General mathematicsCrossref
Mesoscopic learning dynamics of extensive-width neural networks
Shu Zhou, Jean Barbier, Sebastian Goldt
arXiv16 Oct 2026PreprintarXiv licenceFull textStatistics Condensed matterarXiv
Nonlinear Maps Between Irreducible Representations in Graph Neural Networks
Mani Shayestehfar
arXiv29 Oct 2026PreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeX RIS

BibTeX

@misc{ghalem2026learning,
  title = {{Learning SOCP Solver Dynamics with Graph Neural Networks}},
  author = {Adam Ghalem and Lou Salaün and Davide Rinaldi and Fragkiskos D. Malliaros},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26285},
  eprint = {2610.26285},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26285},
  note = {CC BY-NC-ND 4.0},
}

RIS

TY  - UNPB
TI  - Learning SOCP Solver Dynamics with Graph Neural Networks
AU  - Adam Ghalem
AU  - Lou Salaün
AU  - Davide Rinaldi
AU  - Fragkiskos D. Malliaros
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.26285
UR  - https://arxiv.org/abs/2610.26285
AB  - Second-order cone programs (SOCPs) are a fundamental class of convex optimization problems widely applied across engineering domains. Classical interior-point methods are robust and accurate, but their iterative nature can be costly in real-time or repeated-solve settings. This has motivated learning-based solvers that approximate optimizer solutions with neural networks. Recent work has increasingly studied graph neural networks (GNNs) for linear, quadratic, and second-order cone optimization, leveraging their ability to model sparse relational structure among variables, constraints, and objective functions. Most existing GNN-based solvers compress the optimization process into a single forward pass, predicting the optimizer directly without using the intermediate trajectory produced by classical solvers. We introduce SOCPNet, a recursive GNN framework that uses solver trajectories to learn an iterative SOCP solution procedure. A shared GNN model is applied repeatedly, refining the current iterate at each step and enabling inference for a variable number of iterations. Rather than predicting the solution in a single pass, SOCPNet learns from intermediate iterates to progressively refine its estimates using a trajectory-regularized training procedure. We evaluate SOCPNet on multiple datasets spanning standard SOCP problem classes and show that it consistently reduces the final solution error relative to a SOCP-GNN baseline. Finally, we demonstrate how trained SOCPNet models can be used in a hybrid optimization pipeline by warm-starting a classical interior-point solver, reducing solver iterations without loss of accuracy.
ER  -

Abstract

Related

Cite