标题： FSNet：具有保证的约束优化可行性寻求神经网络 显示英文标题

标题： FSNet: Feasibility-Seeking Neural Network for Constrained Optimization with Guarantees

摘要： 高效求解约束优化问题是众多实际应用中的关键所在，然而传统求解器往往在实时使用时计算成本过高。基于机器学习的方法作为一种有前景的替代方案，能够以更快的速度提供近似解，但它们难以严格满足约束条件，导致实践中产生不可行解。为了解决这一问题，我们提出了可行性搜索集成神经网络（FSNet），该方法直接在其求解过程中嵌入了可行性搜索步骤，以确保约束满足。 此可行性搜索步骤通过解决一个无约束优化问题，以可微的方式最小化约束违反量，从而实现端到端训练，并保证可行性和收敛性。 我们的实验涵盖了多种不同的优化问题，包括平滑/非平滑和凸/非凸问题，结果表明，FSNet 能够以显著更快的速度提供与传统求解器相当（甚至在某些情况下更优）的可行解。 显示英文摘要

摘要： Efficiently solving constrained optimization problems is crucial for numerous real-world applications, yet traditional solvers are often computationally prohibitive for real-time use. Machine learning-based approaches have emerged as a promising alternative to provide approximate solutions at faster speeds, but they struggle to strictly enforce constraints, leading to infeasible solutions in practice. To address this, we propose the Feasibility-Seeking-Integrated Neural Network (FSNet), which integrates a feasibility-seeking step directly into its solution procedure to ensure constraint satisfaction. This feasibility-seeking step solves an unconstrained optimization problem that minimizes constraint violations in a differentiable manner, enabling end-to-end training and providing guarantees on feasibility and convergence. Our experiments across a range of different optimization problems, including both smooth/nonsmooth and convex/nonconvex problems, demonstrate that FSNet can provide feasible solutions with solution quality comparable to (or in some cases better than) traditional solvers, at significantly faster speeds.