2025/08/16 by Xiong, Jinxin, Xiqi Gao, Gao, Xi +8 · 1 citation
Computer Science · Mathematics · #Artificial neural network #Convergence (economics) #Convex optimization #FOS: Mathematics #Field (mathematics) #Linear programming #Matrix Theory and Algorithms #Numerical Methods and Algorithms #Optimization and Control (math.OC) #Quadratic equation #Quadratic programming #Regular polygon #Scalability #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2508.11869
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.