Zero-Inertia Limit: From Particle Swarm Optimization to Consensus-Based Optimization

Recently a continuous description of particle swarm optimization (PSO) based on system stochastic differential equations was proposed by Grassi and Pareschi in [Math. Models Methods Appl. Sci., 31 (2021), pp. 1625--1657] where the authors formally showed link between PSO consensus-based (CBO) through zero-inertia limit. This paper is devoted to solving this theoretical open problem [S. L. Pareschi, Math. providing rigorous derivation CBO from limit zero inertia, quantified convergence rate obtained as well. The proofs are probabilistic approach investigating both weak strong corresponding Mckean type path space results illustrated with some numerical examples.