The real-time solution of parametric optimization problems is critical for applications that demand high accuracy under tight real-time constraints, such as model predictive control. To this end, this work presents a learning-based iterative solver for constrained optimization, comprising a neural network predictor that generates initial primal-dual solution estimates, followed by a learned iterative solver that refines these estimates to reach high accuracy. We introduce a novel loss function based on Karush-Kuhn-Tucker (KKT) optimality conditions, enabling fully self-supervised training without pre-solved optimizer solutions. Theoretical guarantees ensure that the training loss function attains minima exclusively at KKT points. A convexification procedure enables application to nonconvex problems while preserving these guarantees. Experiments on two nonconvex case studies demonstrate speedups of up to one order of magnitude compared to state-of-the-art solvers such as IPOPT, while achieving orders of magnitude higher accuracy than competing learning-based approaches.

翻译：参数优化问题的实时求解在需要高精度且受严格实时约束的应用中至关重要，例如模型预测控制。为此，本文提出一种基于学习的约束优化迭代求解器，包含一个用于生成初始原始-对偶解估计的神经网络预测器，以及一个用于细化这些估计以达到高精度的学习型迭代求解器。我们引入了一种基于Karush-Kuhn-Tucker（KKT）最优性条件的新型损失函数，从而无需预先求解的优化器解即可实现完全自监督训练。理论保证确保训练损失函数仅在KKT点处取得极小值。一种凸化过程使得该方法能应用于非凸问题，同时保持上述保证。在两个非凸案例研究中的实验表明，与IPOPT等最先进求解器相比，加速比高达一个数量级，同时与基于学习的竞争方法相比，精度高出多个数量级。