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Akang Wang

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9 papers

2 author rows

TMLR Journal 2025 Journal Article

On Representing Convex Quadratically Constrained Quadratic Programs via Graph Neural Networks

Chenyang Wu
Qian Chen
Akang Wang
Tian Ding
Ruoyu Sun
Wenguo Yang
Qingjiang Shi

Convex quadratically constrained quadratic programs (QCQPs) involve finding a solution within a convex feasible region defined by quadratic constraints while minimizing a convex quadratic objective function. These problems arise in various industrial applications, including power systems and signal processing. Traditional methods for solving convex QCQPs primarily rely on matrix factorization, which quickly becomes computationally prohibitive as the problem size increases. Recently, graph neural networks (GNNs) have gained attention for their potential in representing and solving various optimization problems such as linear programs and linearly constrained quadratic programs. In this work, we investigate the representation power of GNNs in the context of QCQP tasks. Specifically, we propose a new tripartite graph representation for general convex QCQPs and properly associate it with message-passing GNNs. We demonstrate that there exist GNNs capable of reliably representing key properties of convex QCQPs, including feasibility, optimal value, and optimal solution. Our result deepens the understanding of the connection between QCQPs and GNNs, paving the way for future machine learning approaches to efficiently solve QCQPs.

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NeurIPS Conference 2025 Conference Paper

QuadEnhancer: Leveraging Quadratic Transformations to Enhance Deep Neural Networks

Qian Chen
Linxin Yang
Akang Wang
Xiaodong Luo
Yin Zhang

The combination of linear transformations and nonlinear activation functions forms the foundation of most modern deep neural networks, enabling them to approximate highly complex functions. This paper explores the introduction of quadratic transformations to further increase the nonlinearity of the model, with the aim of enhancing the performance of existing architectures. To minimize the additional parameters and computational burden, we propose a lightweight quadratic enhancer that leverages matrix decomposition, weight sharing, and sparsification techniques. This approach introduces only a minimal and negligible increase in parameters and forward computation, while still yielding substantial improvements in model performance. We evaluate the effectiveness of the proposed method across three tasks: text classification, image classification, and fine-tuning large language models (LLMs). In all tasks, our approach demonstrates significant performance gains.

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ICML Conference 2025 Conference Paper

ROS: A GNN-based Relax-Optimize-and-Sample Framework for Max-k-Cut Problems

Yeqing Qiu
Ye Xue
Akang Wang
Yiheng Wang
Qingjiang Shi
Zhi-Quan Luo

The Max-$k$-Cut problem is a fundamental combinatorial optimization challenge that generalizes the classic $\mathcal{NP}$-complete Max-Cut problem. While relaxation techniques are commonly employed to tackle Max-$k$-Cut, they often lack guarantees of equivalence between the solutions of the original problem and its relaxation. To address this issue, we introduce the Relax-Optimize-and-Sample (ROS) framework. In particular, we begin by relaxing the discrete constraints to the continuous probability simplex form. Next, we pre-train and fine-tune a graph neural network model to efficiently optimize the relaxed problem. Subsequently, we propose a sampling-based construction algorithm to map the continuous solution back to a high-quality Max-$k$-Cut solution. By integrating geometric landscape analysis with statistical theory, we establish the consistency of function values between the continuous solution and its mapped counterpart. Extensive experimental results on random regular graphs and the Gset benchmark demonstrate that the proposed ROS framework effectively scales to large instances with up to $20, 000$ nodes in just a few seconds, outperforming state-of-the-art algorithms. Furthermore, ROS exhibits strong generalization capabilities across both in-distribution and out-of-distribution instances, underscoring its effectiveness for large-scale optimization tasks.

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TMLR Journal 2025 Journal Article

Solving Quadratic Programs via Deep Unrolled Douglas-Rachford Splitting

Jinxin Xiong
Xi Gao
Linxin Yang
Jiang Xue
Xiaodong Luo
Akang Wang

Convex quadratic programs (QPs) are fundamental to numerous applications, including finance, engineering, and energy systems. Among the various methods for solving them, the Douglas-Rachford (DR) splitting algorithm is notable for its robust convergence properties. Concurrently, the emerging field of Learning-to-Optimize offers promising avenues for enhancing algorithmic performance, with algorithm unrolling receiving considerable attention due to its computational efficiency and interpretability. In this work, we propose an approach that unrolls a modified DR splitting algorithm to efficiently learn solutions for convex QPs. Specifically, we introduce a tailored DR splitting algorithm that replaces the computationally expensive linear system-solving step with a simplified gradient-based update, while retaining convergence guarantees. Consequently, we unroll the resulting DR splitting method and present a well-crafted neural network architecture to predict QP solutions. Our method achieves up to 50% reductions in iteration counts and 40% in solve time across benchmarks on both synthetic and real-world QP datasets, demonstrating its scalability and superior performance in enhancing computational efficiency across varying sizes.

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ICLR Conference 2025 Conference Paper

When GNNs meet symmetry in ILPs: an orbit-based feature augmentation approach

Qian Chen
Lei Li 0030
Qian Li
Jianghua Wu
Akang Wang
Ruoyu Sun 0001
Xiaodong Luo
Tsung-Hui Chang

A common characteristic in integer linear programs (ILPs) is symmetry, allowing variables to be permuted without altering the underlying problem structure. Recently, GNNs have emerged as a promising approach for solving ILPs. However, a significant challenge arises when applying GNNs to ILPs with symmetry: classic GNN architectures struggle to differentiate between symmetric variables, which limits their predictive accuracy. In this work, we investigate the properties of permutation equivalence and invariance in GNNs, particularly in relation to the inherent symmetry of ILP formulations. We reveal that the interaction between these two factors contributes to the difficulty of distinguishing between symmetric variables. To address this challenge, we explore the potential of feature augmentation and propose several guiding principles for constructing augmented features. Building on these principles, we develop an orbit-based augmentation scheme that first groups symmetric variables and then samples augmented features for each group from a discrete uniform distribution. Empirical results demonstrate that our proposed approach significantly enhances both training efficiency and predictive performance.

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NeurIPS Conference 2024 Conference Paper

IPM-LSTM: A Learning-Based Interior Point Method for Solving Nonlinear Programs

Xi Gao
Jinxin Xiong
Akang Wang
Qihong Duan
Jiang Xue
Qingjiang Shi

Solving constrained nonlinear programs (NLPs) is of great importance in various domains such as power systems, robotics, and wireless communication networks. One widely used approach for addressing NLPs is the interior point method (IPM). The most computationally expensive procedure in IPMs is to solve systems of linear equations via matrix factorization. Recently, machine learning techniques have been adopted to expedite classic optimization algorithms. In this work, we propose using Long Short-Term Memory (LSTM) neural networks to approximate the solution of linear systems and integrate this approximating step into an IPM. The resulting approximate NLP solution is then utilized to warm-start an interior point solver. Experiments on various types of NLPs, including Quadratic Programs and Quadratically Constrained Quadratic Programs, show that our approach can significantly accelerate NLP solving, reducing iterations by up to 60% and solution time by up to 70% compared to the default solver.

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ICML Conference 2024 Conference Paper

PDHG-Unrolled Learning-to-Optimize Method for Large-Scale Linear Programming

Bingheng Li
Linxin Yang
Yupeng Chen
Senmiao Wang
Haitao Mao
Qian Chen
Yao Ma 0001
Akang Wang

Solving large-scale linear programming (LP) problems is an important task in various areas such as communication networks, power systems, finance and logistics. Recently, two distinct approaches have emerged to expedite LP solving: (i) First-order methods (FOMs); (ii) Learning to optimize (L2O). In this work, we propose an FOM-unrolled neural network (NN) called PDHG-Net, and propose a two-stage L2O method to solve large-scale LP problems. The new architecture PDHG-Net is designed by unrolling the recently emerged PDHG method into a neural network, combined with channel-expansion techniques borrowed from graph neural networks. We prove that the proposed PDHG-Net can recover PDHG algorithm, thus can approximate optimal solutions of LP instances with a polynomial number of neurons. We propose a two-stage inference approach: first use PDHG-Net to generate an approximate solution, and then apply PDHG algorithm to further improve the solution. Experiments show that our approach can significantly accelerate LP solving, achieving up to a 3$\times$ speedup compared to FOMs for large-scale LP problems.

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NeurIPS Conference 2024 Conference Paper

SymILO: A Symmetry-Aware Learning Framework for Integer Linear Optimization

Qian Chen
Tianjian Zhang
Linxin Yang
Qingyu Han
Akang Wang
Ruoyu Sun
Xiaodong Luo
Tsung-Hui Chang

Integer linear programs (ILPs) are commonly employed to model diverse practical problems such as scheduling and planning. Recently, machine learning techniques have been utilized to solve ILPs. A straightforward idea is to train a model via supervised learning, with an ILP as the input and an optimal solution as the label. An ILP is symmetric if its variables can be permuted without changing the problem structure, resulting in numerous equivalent and optimal solutions. Randomly selecting an optimal solution as the label can introduce variability in the training data, which may hinder the model from learning stable patterns. In this work, we incorporate the intrinsic symmetry of ILPs and propose a novel training framework called SymILO. Specifically, we modify the learning task by introducing solution permutation along with neural network weights as learnable parameters and then design an alternating algorithm to jointly optimize the loss function. We conduct extensive experiments on ILPs involving different symmetries and the computational results demonstrate that our symmetry-aware approach significantly outperforms three existing methods----achieving $50. 3\\%$, $66. 5\\%$, and $45. 4\\%$ average improvements, respectively.

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ICLR Conference 2023 Conference Paper

A GNN-Guided Predict-and-Search Framework for Mixed-Integer Linear Programming

Qingyu Han
Linxin Yang
Qian Chen
Xiang Zhou
Dong Zhang
Akang Wang
Ruoyu Sun 0001
Xiaodong Luo

Mixed-integer linear programming (MILP) is widely employed for modeling combinatorial optimization problems. In practice, similar MILP instances with only coefficient variations are routinely solved, and machine learning (ML) algorithms are capable of capturing common patterns across these MILP instances. In this work, we combine ML with optimization and propose a novel predict-and-search framework for efficiently identifying high-quality feasible solutions. Specifically, we first utilize graph neural networks to predict the marginal probability of each variable, and then search for the best feasible solution within a properly defined ball around the predicted solution. We conduct extensive experiments on public datasets, and computational results demonstrate that our proposed framework achieves 51.1% and 9.9% performance improvements to MILP solvers SCIP and Gurobi on primal gaps, respectively.

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