Faithful global convergence for the rescaled Consensus-Based Optimization

2025/03/11 by Hui Huang, Huang, Hui, Hicham Kouhkouh +3 · 1 citation
Mathematics · #Advanced Optimization Algorithms Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2503.08578

openalex publication_date 2025/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyze the Consensus-Based Optimization (CBO) algorithm with a consensus point rescaled by a small fixed parameter κ∈ (0,1). 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 both the time--horizon t → ∞ and the inverse--temperature α→ ∞, providing a rigorous theoretical foundation for the algorithm's global convergence. Furthermore, our findings extend to the case of multiple and non--discrete set of minimizers.

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