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，旨在解决具有等式约束的最小化问题，特别适用于损失函数呈现不可微或非凸特性的情况。该方法将基于共识的优化算法组件与针对约束集合引入的新型强迫项相结合。推导了粒子系统的严格平均场极限，并建立了该平均场极限向约束最小化器的收敛性。此外，我们引入了一种稳定的离散化算法，并通过多种数值实验展示了所提方法的性能。