AT-SKM-Net：面向动态图线性硬约束的加速可行求解框架
AT-SKM-Net: An Accelerated Trainable Sampling Kaczmarz-Motzkin Framework for Linear Hard-Constraint Feasibility on Dynamic Graphs
一篇硬核优化论文：用 GNN 加 Cholesky Update 求动态图上的硬约束问题，迭代少了 85%，速度最高快 7 倍多，做电力或管网调度的朋友可以看看。
论文提出 AT-SKM-Net 框架，针对图结构优化中大量严格硬约束导致的计算瓶颈。它用拓扑感知异构 GNN 引导混合采样策略，把计算集中在活跃约束上；并用 Cholesky Update 机制在低秩扰动下将等式投影复杂度从 O(N^3) 降到 O(N^2)。在随机几何图、N-1 安全约束 DC-OPF 和最小成本天然气输运问题上，迭代次数最多减少 85%，SKM 层加速 2.95x-7.29x，同时保持零约束违反。
AT-SKM-Net: An Accelerated Trainable Sampling Kaczmarz-Motzkin Framework for Linear Hard-Constraint Feasibility on Dynamic Graphs
Graph-structured optimization with linear constraints is fundamental to critical infrastructure but faces scalability limits due to massive strict hard constraints and high dimensionality. While recent projection-based methods such as Trainable Sampling Kaczmarz-Motzkin Net (T-SKM-Net) guarantee feasibility, they face high computational costs in dynamic environments by processing the entire constraint set and requiring expensive matrix factorizations. To bridge this gap, we propose the Accelerated Trainable-SKM (AT-SKM) Net framework. To concentrate computation on the active constraints and eliminate redundant calculations, we introduce a hybrid sampling strategy guided by a topology-aware heterogeneous GNN model. To efficiently handle topological shifts in graph-based constraints, we employ a Cholesky Update mechanism that theoretically reduces the equality projection complexity from O(N^3) to O(N^2) under low-rank perturbations. Experiments on random geometric graphs, N-1 Security-Constrained DC-OPF, and minimum-cost gas transport problem demonstrate that AT-SKM reduces iteration counts by up to 85% and achieves 2.95x-7.29x SKM layer speedups, while maintaining zero constraint violations.
