Recently, Li Ruizhe, an undergraduate student (Class of 2022) in the Department of Mathematics at the Southern University of Science and Technology, collaborated with Liang Enming, a Research Assistant Professor at the City University of Hong Kong, and Chen Minghua, a Presidential Chair Professor at The Chinese University of Hong Kong, Shenzhen. The team conducted research on the theory and methods of using Graph Neural Networks (GNNs) to solve optimization problems. Their findings have been accepted by the International Conference on Learning Representations (ICLR 2026), a top-tier international conference in the field of artificial intelligence. 

The graph representation of SOCPs and the message-passing steps in GNN design

Second Order Cone Programming (SOCP) represents a fundamental class of convex optimization problems with numerous real-world applications, including optimal power flow, trajectory planning, image restoration, and network localization. However, traditional algorithms, such as primal-dual interior point methods, face computational limitations in large-scale applications, particularly in real-time scenarios where rapid response is crucial. Recent advances in machine learning, such as the learning-to-optimize (L2O) paradigm, have enabled solving optimization problems in real-time. Specifically, GNNs have been proven efficient by leveraging the inherent graph structures of the problem. Although existing research has demonstrated that GNNs can approximate feasibility and optimal solution mappings for specific optimization problems (such as Linear Programming and Convex Quadratic Programming), generalizing these theories to more general Second-Order Cone Programs (SOCPs) remains challenging. Second-order cone constraints involve both linear terms and non-linear norm terms, making their structures difficult to effectively express and analyze. To address these challenges, the research team proposed a novel graph representation method that decomposes the structure of conic constraints into interactions between intrinsic linear relations. Based on this, they designed SOCP-GNN, a model equipped with universal approximation theoretical guarantees. SOCP-GNN is capable of approximating key properties probably and approximately, such as the feasibility and optimal solutions of SOCPs. Furthermore, this framework naturally extends to arbitrary p-order cone programs (where p≥1) without GNN structural modifications.  Additionally, the team provided the first analysis of the sample complexity of GNNs in 'learning to optimize' tasks, based on Rademacher complexity. Experimental results demonstrate that the proposed method achieves superior performance on both synthetic data and power grid optimization tasks.

The paper is titled: “On the Universality and Complexity of GNN for Solving Second-order Cone Programs."Li Ruizhe is the sole first author of the paper, with Assistant Professor Enming Liang and Chair Professor Minghua Chen serving as the corresponding authors. The Southern University of Science and Technology (SUSTech) is the first author’s affiliation.

Remarks: Founded in 2013 by Turing Award laureates Yoshua Bengio and Yann LeCun, the International Conference on Learning Representations (ICLR) is a premier international academic conference focused on cutting-edge fields such as representation learning, deep learning, reinforcement learning, generative models, and large language models. Recognized alongside NeurIPS and ICML as one of the three top-tier conferences in machine learning, ICLR consistently ranks at the forefront of Google Scholar’s impact rankings for artificial intelligence conferences.

Link to the paper: https://openreview.net/pdf?id=wFttcDu6Fr