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HUANet advances the field of AI for scientific computing by integrating hard constraints and optimality conditions directly into unrolled ADMM iterations, ensuring reliable solutions for parametric convex optimization problems. This approach moves beyond black-box learning to guarantee constraint satisfaction while accelerating convergence in control applications and benchmark scenarios.
HUANet: Hard-Constrained Unrolled ADMM for Constrained Convex Optimization
arXiv:2604.13179v2 Announce Type: replace-cross Abstract: This paper presents HUANet, a constrained deep neural network architecture that unrolls the Alternating Direction Method of Multipliers (ADMM) into a trainable neural network for accelerating parametric constrained convex optimization. Existing end-to-end learning methods operate as black-box mappings from parameters to solutions, often without explicitly incorporating optimality principles or guaranteeing constraint satisfaction. To address these limitations, HUANet embeds a hard-constrained neural network within each unrolled ADMM iteration, where a differentiable correction stage enforces the affine equalities of the primal subproblem. Furthermore, we incorporate first-order optimality conditions into a self-supervised training loss to promote the convergence of the proposed unrolled algorithm. Extensive numerical experiments for benchmark optimization problems and a control application demonstrate and validate the effectiveness of HUANet in accelerating constrained convex optimization solving.
Abstract:This paper presents HUANet, a constrained deep neural network architecture that unrolls the Alternating Direction Method of Multipliers (ADMM) into a trainable neural network for accelerating parametric constrained convex optimization. Existing end-to-end learning methods operate as black-box mappings from parameters to solutions, often without explicitly incorporating optimality principles or guaranteeing constraint satisfaction. To address these limitations, HUANet embeds a hard-constrained neural network within each unrolled ADMM iteration, where a differentiable correction stage enforces the affine equalities of the primal subproblem. Furthermore, we incorporate first-order optimality conditions into a self-supervised training loss to promote the convergence of the proposed unrolled algorithm. Extensive numerical experiments for benchmark optimization problems and a control application demonstrate and validate the effectiveness of HUANet in accelerating constrained convex optimization solving.
Optimization and Control (math.OC); Machine Learning (cs.LG); Systems and Control (eess.SY)
arXiv:2604.13179 [math.OC]
(or arXiv:2604.13179v2 [math.OC] for this version)
https://doi.org/10.48550/arXiv.2604.13179 Focus to learn more arXiv-issued DOI via DataCite
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