用可学习网络加速带约束的凸优化求解
HUANet: Hard-Constrained Unrolled ADMM for Constrained Convex Optimization
- 将ADMM迭代展开为可训练神经网络，每步强制满足等式约束
- 通过可微修正层确保约束硬性满足，提升求解精度
- 融合一阶最优性条件作为软约束，加快收敛速度
本文提出HUANet，一种将交替方向乘子法（ADMM）迭代展开为可训练神经网络的约束型深度网络架构，用于求解带约束的凸优化问题。现有端到端学习方法通常作为黑箱映射，缺乏显式最优性原则且难以保证约束。为解决此问题，我们展开ADMM并在每轮迭代中嵌入硬约束神经网络，通过网络输出的可微修正阶段强制满足等式约束。此外，训练过程中引入一阶最优性条件作为软约束，以促进所提展开算法的收敛性。大量数值实验验证了该架构在约束优化问题上的有效性。
原文摘要 · Abstract (English)
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.
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