HUANet: Hard-Constrained Unrolled ADMM for Constrained Convex Optimization

TL;DR

HUANet is a novel neural network architecture that unrolls ADMM iterations with hard constraints and optimality conditions, enabling efficient solutions to constrained convex optimization problems.

Contribution

It introduces a trainable unrolled ADMM-based neural network with explicit constraint enforcement and convergence-promoting training strategies.

Findings

Validated effectiveness on constrained optimization tasks

Achieved accelerated convergence compared to traditional methods

Successfully enforced equality constraints via differentiable correction

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.