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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.09391 |
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| _version_ | 1866910943745671168 |
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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 |