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Main Authors: Gao, Xi, Xiong, Jinxin, Yang, Linxin, Wang, Akang, Xu, Weiwei, Xue, Jiang
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2505.09391
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author Gao, Xi
Xiong, Jinxin
Yang, Linxin
Wang, Akang
Xu, Weiwei
Xue, Jiang
author_facet Gao, Xi
Xiong, Jinxin
Yang, Linxin
Wang, Akang
Xu, Weiwei
Xue, Jiang
contents Convex quadratic programs (QPs) constitute a fundamental computational primitive across diverse domains including financial optimization, control systems, and machine learning. The alternating direction method of multipliers (ADMM) has emerged as a preferred first-order approach due to its iteration efficiency - exemplified by the state-of-the-art OSQP solver. Machine learning-enhanced optimization algorithms have recently demonstrated significant success in speeding up the solving process. This work introduces a neural-accelerated ADMM variant that replaces exact subproblem solutions with learned approximations through a parameter-efficient Long Short-Term Memory (LSTM) network. We derive convergence guarantees within the inexact ADMM formalism, establishing that our learning-augmented method maintains primal-dual convergence while satisfying residual thresholds. Extensive experimental results demonstrate that our approach achieves superior solution accuracy compared to existing learning-based methods while delivering significant computational speedups of up to $7\times$, $28\times$, and $22\times$ over Gurobi, SCS, and OSQP, respectively. Furthermore, the proposed method outperforms other learning-to-optimize methods in terms of solution quality. Detailed performance analysis confirms near-perfect compliance with the theoretical assumptions, consequently ensuring algorithm convergence.
format Preprint
id arxiv_https___arxiv_org_abs_2505_09391
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Learning-Based Inexact ADMM for Solving Quadratic Programs
Gao, Xi
Xiong, Jinxin
Yang, Linxin
Wang, Akang
Xu, Weiwei
Xue, Jiang
Optimization and Control
Convex quadratic programs (QPs) constitute a fundamental computational primitive across diverse domains including financial optimization, control systems, and machine learning. The alternating direction method of multipliers (ADMM) has emerged as a preferred first-order approach due to its iteration efficiency - exemplified by the state-of-the-art OSQP solver. Machine learning-enhanced optimization algorithms have recently demonstrated significant success in speeding up the solving process. This work introduces a neural-accelerated ADMM variant that replaces exact subproblem solutions with learned approximations through a parameter-efficient Long Short-Term Memory (LSTM) network. We derive convergence guarantees within the inexact ADMM formalism, establishing that our learning-augmented method maintains primal-dual convergence while satisfying residual thresholds. Extensive experimental results demonstrate that our approach achieves superior solution accuracy compared to existing learning-based methods while delivering significant computational speedups of up to $7\times$, $28\times$, and $22\times$ over Gurobi, SCS, and OSQP, respectively. Furthermore, the proposed method outperforms other learning-to-optimize methods in terms of solution quality. Detailed performance analysis confirms near-perfect compliance with the theoretical assumptions, consequently ensuring algorithm convergence.
title A Learning-Based Inexact ADMM for Solving Quadratic Programs
topic Optimization and Control
url https://arxiv.org/abs/2505.09391