Convex-SKM-Net：面向神经凸约束满足的低延迟块半空间修正层
Convex-SKM-Net: Low-Latency Block Halfspace Corrections for Neural Convex Constraint Satisfaction
一个能塞进神经网络的凸约束修正层，SOC-MPC 推理快了 144 倍还保证可行性，做优化控制或电力系统调度的可以看看实现思路。
论文提出 Convex-SKM-Net，一个凸约束满足层，通过残差与（次）梯度预言机构造线性化半空间，无需约束特定的不等式投影器。它用固定深度的对偶投影梯度下降求解最小位移块问题，且全程采用 GPU 友好的矩阵运算。论文证明了固定对偶深度下外层迭代的收敛性，并在 Slater 条件与有界次梯度下给出线性收敛率。在三个二阶锥模型预测控制（SOC-MPC）时域和六个电力系统凸松弛基准上，全部测试输出满足 10^-3 可行性容差。与最新约束满足方法相比，SOC-MPC 推理加速最高达 144.3 倍，QCQP 基准加速 7.7 倍，QCQP 平均目标差距仅 0.012%，且联合训练的可学习 mobility 将五种子仿射任务平均差距降低 22.4%。
Convex-SKM-Net: Low-Latency Block Halfspace Corrections for Neural Convex Constraint Satisfaction
Fast inference and strict constraint satisfaction are essential for learning-based decision-making. Existing methods often rely on constraint-specific projections or feasible-set parameterizations, while iterative repair can be costly. We introduce Convex-SKM-Net, a convex constraint-satisfaction layer that forms linearization halfspaces from residual and (sub)gradient oracles without constraint-specific inequality projectors. It applies fixed-depth dual projected-gradient descent (dual PGD) to minimum-displacement block problems using GPU-friendly matrix operations. We jointly learn the predictor and a positive-definite mobility, adapting the correction geometry to improve objective quality. We prove convergence of the outer iterates at fixed dual depth and linear convergence in distance under Slater's condition and bounded subgradients. All our test outputs on three second-order-cone model-predictive control (SOC-MPC) horizons and six power-system convex relaxations satisfy a $10^{-3}$ feasibility tolerance. Comparisons with the latest constraint-satisfaction methods show inference speedups of up to $144.3\times$ on SOC-MPC and $7.7\times$ on a convex quadratically constrained quadratic programming (QCQP) benchmark with joint training. On QCQP, the mean objective gap is $0.012\%$, with full test feasibility at $10^{-4}$. Learning mobility reduces the five-seed affine-task mean gap by $22.4\%$ and improves gaps in matched power-system comparisons.