用神经网络求解带约束的优化问题，精度和收敛速度均优于现有方法。
Learning based convex approximation for constrained parametric optimization
- 用输入凸神经网络结合增广拉格朗日法，自监督训练求解约束优化。
- 在二次规划、非凸优化等任务上，可行性与最优性差距更小，收敛更快。
- 适合需要快速高精度求解约束优化的工程场景，如电力系统调度。
我们提出一种基于输入凸神经网络（ICNN）的自监督学习框架，用于求解连续约束优化问题。通过融合增广拉格朗日法（ALM）与约束修正机制，该框架实现了非严格约束可行性、更优的最优性间隙以及相较于现有学习型方法的最佳收敛速率。我们提供了严格的收敛性分析，证明即使内部求解器为神经网络，算法仍可收敛至原问题的卡鲁什-库恩-塔克（KKT）点，且近似误差有界。我们在一系列基准任务上进行了测试，包括二次规划（QP）、非凸规划及大规模交流最优潮流（AC OPF）问题。结果表明，相较于现有求解器（如OSQP、IPOPT）及最新学习型方法（如DC3、PDL），本方法在准确性、可行性与计算效率之间取得了更优平衡。
原文摘要 · Abstract (English)
We propose an input convex neural network (ICNN)-based self-supervised learning framework to solve continuous constrained optimization problems. By integrating the augmented Lagrangian method (ALM) with the constraint correction mechanism, our framework ensures \emph{non-strict constraint feasibility}, \emph{better optimality gap}, and \emph{best convergence rate} with respect to the state-of-the-art learning-based methods. We provide a rigorous convergence analysis, showing that the algorithm converges to a Karush-Kuhn-Tucker (KKT) point of the original problem even when the internal solver is a neural network, and the approximation error is bounded. We test our approach on a range of benchmark tasks including quadratic programming (QP), nonconvex programming, and large-scale AC optimal power flow problems. The results demonstrate that compared to existing solvers (e.g., \texttt{OSQP}, \texttt{IPOPT}) and the latest learning-based methods (e.g., DC3, PDL), our approach achieves a superior balance among accuracy, feasibility, and computational efficiency.
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