用分阶段残差网络提升约束优化中高优先级约束的满足度。
Multi-ResNets for Subspace Preconditioning in Constrained Optimization
- 分阶段设计残差网络，按优先级逐层处理约束条件。
- 在合成与实际电力系统测试中，高优先级约束违反显著降低。
- 适合需严格满足关键约束的工程优化问题，如电网调度。
我们提出MResOpt，一种用于约束优化问题的分阶段残差神经网络架构。该架构融入预测-补全-修正流程，通过中间补全和阶段感知损失实现按优先级分解约束满足。框架支持领域知识引导的有序约束满足，可利用存在的序结构。在理想无限宽假设下，其行为等价于序列高斯过程回归。在合成二次规划（QP）、二次约束二次规划（QCQP）和二阶锥规划（SOCP）基准上，该分阶段架构在凸与非凸设置下均提升了高优先级约束的满足度。在含线路潮流约束的交流最优功率流问题中，我们引入物理启发的约束排序，并证明MResOpt能实现学习型任务分工，使迭代点保持在等式流形上，相比重投影基线方法显著降低高优先级违反，同时保持计算高效。
原文摘要 · Abstract (English)
We propose MResOpt, a staged residual neural network architecture for constrained optimization problems. Our architecture fits within predict-complete-correct pipelines and decomposes constraint satisfaction by priority through intermediate re-completion and stage-aware losses. The framework enables domain-informed ordered constraint satisfaction which allows the network to utilize ordinal structure when present. Under an idealized infinite-width regime, we show that our design behaves as sequential Gaussian Process regression. On synthetic QP, QCQP, and SOCP benchmarks, the staged architecture improves high-priority constraint satisfaction across convex and non-convex settings. On line-flow-constrained AC optimal power flow, we introduce a physics-motivated constraint ordering and show that MResOpt supports a learned division of labor that keeps iterates on the equality manifold, achieving substantially lower high-priority violation than reprojected baselines while remaining computationally efficient.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。