Graph neural networks improve iterative solution of cone programs
Learning SOCP Solver Dynamics with Graph Neural Networks
Machine Learning
Summary
Solving certain math problems called second-order cone programs can take a lot of time, especially when needing quick or repeated answers. The authors propose a new method called SOCPNet that uses graph neural networks to mimic and speed up the step-by-step solving process instead of just guessing the final answer all at once. This approach learns from the sequence of steps a traditional solver takes, improving accuracy over previous methods. Additionally, it can help classical solvers start closer to the solution, saving even more time without losing accuracy.
What this means in practice
- •For control engineers: Speed up repeated or real-time optimization problems by using SOCPNet to quickly refine solutions in second-order cone programs.
- •For energy grid operators: Improve efficiency of power flow optimizations by reducing iterations of classical solvers through warm-starting with SOCPNet predictions.
Authors
Adam Ghalem, Lou Salaün, Davide Rinaldi, Fragkiskos D. Malliaros
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.