Convex-SKM-Net: Low-Latency Block Halfspace Corrections for Neural Convex Constraint Satisfaction

Convex‑SKM‑Net is a neural layer that enforces convex constraints by constructing linearization halfspaces from residual and gradient oracles, avoiding constraint‑specific projections. It uses fixed‑depth dual projected‑gradient descent on GPU‑friendly matrix operations to solve minimum‑displacement block problems, jointly learning a predictor and a positive‑definite mobility matrix to shape corrections. The method converges theoretically, achieves sub‑$10^{-3}$ feasibility on SOC‑MPC and power‑system relaxations, and outperforms state‑of‑the‑art constraint‑satisfaction techniques with up to 144× speedups and near‑optimal objective gaps.

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