This talk addresses the global 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 has been derived, the convergence of the mean-field limit to the constrained minimizer has been established. Additionally, we introduce a stable discretized algorithm and conduct various numerical experiments to illustrate the performance of the proposed method.