HUANet: Hard-Constrained Unrolled ADMM for Constrained Convex Optimization

2026-04-14

AI Summary

Existing end-to-end approaches to solving constrained convex optimization problems often fail to strictly satisfy constraints and lack guarantees of optimality. This work proposes a trainable architecture based on unfolded ADMM that enforces hard constraints through an embedded constraint-satisfaction module and a differentiable equality-constraint correction layer, ensuring exact feasibility at every iteration. Furthermore, first-order optimality conditions are incorporated as soft constraints into the training objective to guide convergence toward high-quality solutions. The proposed method uniquely unifies strict constraint satisfaction with optimality-aware learning within an unfolded optimization framework. Empirical results across multiple constrained convex optimization tasks demonstrate substantial improvements over conventional black-box end-to-end models, achieving both high solution accuracy and strong constraint compliance.

Technology Category

• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Computer Vision: Learning & Optimization for CV

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization

Abstract

This paper presents HUANet, a constrained deep neural network architecture that unrolls the iterations of the Alternating Direction Method of Multipliers (ADMM) into a trainable neural network for solving constrained convex optimization problems. Existing end-to-end learning methods operate as black-box mappings from parameters to solutions, often lacking explicit optimality principles and failing to enforce constraints. To address this limitation, we unroll ADMM and embed a hard-constrained neural network at each iteration to accelerate the algorithm, where equality constraints are enforced via a differentiable correction stage at the network output. Furthermore, we incorporate first-order optimality conditions as soft constraints during training to promote the convergence of the proposed unrolled algorithm. Extensive numerical experiments are conducted to validate the effectiveness of the proposed architecture for constrained optimization problems.

Problem

• constrained convex optimization
• end-to-end learning
• constraint satisfaction
• optimality principles
• black-box mapping

Innovation

• unrolled ADMM
• hard-constrained neural network
• constrained convex optimization
• differentiable correction
• optimality conditions