  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.
