This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed method combines components from consensus-based optimization algorithm with a newly introduced forcing term directed at the constraint set. A rigorous mean-field limit of the particle system is derived, and the convergence of the mean-field limit to the constrained minimizer is established. Additionally, we introduce a stable discretized algorithm and conduct various numerical experiments to demonstrate the performance of the proposed method.

翻译：本文提出了一种基于粒子的优化方法，旨在处理带有等式约束的极小化问题，尤其适用于损失函数具有不可微性或非凸性的情形。所提方法将基于共识的优化算法中的组件与新引入的、指向约束集的强制项相结合。推导了该粒子系统的严格平均场极限，并建立了平均场极限收敛到约束极小值点的收敛性。此外，我们介绍了一种稳定的离散算法，并通过多种数值实验验证了所提方法的性能。