On the mean-field limit for the consensus-based optimization

Abstract

This paper is concerned with the large particle limit for the consensus-based optimization (CBO), which was postulated in the pioneering works [6,28]. In order to solve this open problem, we adapt a compactness argument by first proving the tightness of the empirical measures $\{{\mu }^N{\}}_{N\ge 2}$ associated to the particle system and then verifying that the limit measure $\mu$ is the unique weak solution to the mean-field CBO equation. Such results are extended to the model of particle swarm optimization (PSO).

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• Leveraging Memory Effects and Gradient Information in Consensus-Based Optimization: On Global Convergence in Mean-Field Law
• Mean-field limits for Consensus-Based Optimization and Sampling
• Consensus based optimization with memory effects: random selection and applications
• CBX: Python and Julia packages for consensus-based interacting particle methods
• Self-interacting CBO: Existence, uniqueness, and long-time convergence
• A multiscale Consensus-Based algorithm for multi-level optimization
• Consensus-Based Optimization with Truncated Noise
• Uniform-in-time propagation of chaos for the Cucker--Smale model
• Swarm-based optimization with jumps: a kinetic BGK framework and convergence analysis
• Consensus-based algorithms for stochastic optimization problems
• Micro-Macro Decomposition of Particle Swarm Optimization Methods