Faithful Global Convergence for the Rescaled Consensus–Based Optimization

Abstract. We analyze the consensus-based optimization algorithm with a consensus point rescaled by a fixed parameter [Formula: see text]. Under minimal assumptions on the objective function and the initial data, we establish its unconditional convergence to the global minimizer. Our results hold in the asymptotic regime where the time horizon [Formula: see text] and the inverse temperature [Formula: see text] are taken successively, providing a rigorous theoretical foundation for the algorithm’s global convergence. Furthermore, our findings extend to the case of multiple and nondiscrete set of minimizers.