用神经网络快速求解参数化凸优化问题，预测结果满足最优性条件。
KKT-Informed Neural Network
- 基于KKT条件惩罚训练，确保预测解符合最优性要求。
- 在已知参数范围内随机生成训练数据，无需外部标注样本。
- 牺牲理论最优性换取速度提升，适合批量并行求解场景。
本文提出一种基于神经网络的参数化凸优化问题求解方法，通过训练网络在给定一批输入参数时估计最优解。网络训练过程通过惩罚违反Karush-Kuhn-Tucker（KKT）条件的行为来实现，确保预测结果满足最优性准则。由于参数空间的边界已知，训练数据可直接在该区域内随机生成，无需依赖外部数据。该方法以牺牲严格最优性为代价，显著提升求解速度，支持对一类优化问题进行并行求解。
原文摘要 · Abstract (English)
A neural network-based approach for solving parametric convex optimization problems is presented, where the network estimates the optimal points given a batch of input parameters. The network is trained by penalizing violations of the Karush-Kuhn-Tucker (KKT) conditions, ensuring that its predictions adhere to these optimality criteria. Additionally, since the bounds of the parameter space are known, training batches can be randomly generated without requiring external data. This method trades guaranteed optimality for significant improvements in speed, enabling parallel solving of a class of optimization problems.
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