Neural Compression of Long ADMM Trajectory for Multiparametric Quadratic Program
Abstract
Solving large-scale multiparametric quadratic programs (mpQPs) in real time often requires thousands of iterative optimization updates, creating a major computational bottleneck in model predictive control and learning-enabled systems. This paper proposes TQPNet, a self-supervised neural compression framework that learns to compress long ADMM optimization trajectories into a compact neural warm start followed by a few refinement iterations. We derive a low-dimensional ADMM scheme operating on the primal-dual variables (x,β) and show that its iteration admits an equivalent ReLU-layer representation, termed ADMM(ReLU). Building on this insight, TQPNet combines a multilayer perceptron with ReLU activations (MLP(ReLU)) and a small number of unrolled ADMM(ReLU) refinement layers. The network is trained offline using an optimality-condition-informed residual loss, eliminating the need for solver-generated labels. The proposed residual-based framework enables both self-supervised training and online solution certification through adaptive ADMM(ReLU) refinement. Experiments on large-scale mpQPs and real-time MPC applications demonstrate that TQPNet achieves high accuracy, strong generalization, and substantially faster inference than conventional optimization-based methods.
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BibTeX
@misc{wu2026neural,
title = {{Neural Compression of Long ADMM Trajectory for Multiparametric Quadratic Program}},
author = {Liang Wu and Honghui Zheng and Bo Yang and Xu Yang and Yilin Mo and Ján Drgoňa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38079},
eprint = {2610.38079},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38079},
}
RIS
TY - UNPB
TI - Neural Compression of Long ADMM Trajectory for Multiparametric Quadratic Program
AU - Liang Wu
AU - Honghui Zheng
AU - Bo Yang
AU - Xu Yang
AU - Yilin Mo
AU - Ján Drgoňa
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.38079
UR - https://arxiv.org/abs/2610.38079
AB - Solving large-scale multiparametric quadratic programs (mpQPs) in real time often requires thousands of iterative optimization updates, creating a major computational bottleneck in model predictive control and learning-enabled systems. This paper proposes TQPNet, a self-supervised neural compression framework that learns to compress long ADMM optimization trajectories into a compact neural warm start followed by a few refinement iterations. We derive a low-dimensional ADMM scheme operating on the primal-dual variables (x,β) and show that its iteration admits an equivalent ReLU-layer representation, termed ADMM(ReLU). Building on this insight, TQPNet combines a multilayer perceptron with ReLU activations (MLP(ReLU)) and a small number of unrolled ADMM(ReLU) refinement layers. The network is trained offline using an optimality-condition-informed residual loss, eliminating the need for solver-generated labels. The proposed residual-based framework enables both self-supervised training and online solution certification through adaptive ADMM(ReLU) refinement. Experiments on large-scale mpQPs and real-time MPC applications demonstrate that TQPNet achieves high accuracy, strong generalization, and substantially faster inference than conventional optimization-based methods.
ER -