On the mean‐field limit for the consensus‐based optimization
Hui Huang, Jinniao Qiu
Abstract
This paper is concerned with the large particle limit for the consensus‐based optimization (CBO), which was postulated in the pioneering works by Carrillo, Pinnau, Totzeck and many others. In order to solve this open problem, we adapt a compactness argument by first proving the tightness of the empirical measures associated to the particle system and then verifying that the time marginal of the limit measure is the unique weak solution to the mean‐field CBO equation. Such results are further extended to the model of particle swarm optimization (PSO).
Topics & Concepts
Particle swarm optimizationLimit (mathematics)Argument (complex analysis)Compact spaceMeasure (data warehouse)Particle systemMathematical optimizationMathematicsField (mathematics)Empirical measureOrder (exchange)Optimization problemApplied mathematicsStatistical physicsComputer scienceMathematical economicsPhysicsPure mathematicsMathematical analysisStatisticsChemistryFinanceBiochemistryDatabaseEconomicsOperating systemDiffusion and Search DynamicsMarkov Chains and Monte Carlo MethodsDistributed Control Multi-Agent Systems