abstract: Metaheuristic optimization based on multi-agent dynamics has a long history and plays a pivotal role today in many applications, ranging from machine learning to optimal control. In this talk, we will show how the use of kinetic and mean-field techniques enables a rigorous mathematical formulation of such algorithms and permits to prove convergence to the global minimum under mild assumptions on the objective function. In particular, we will focus on analyzing some of the most popular algorithms, such as simulated annealing, genetic algorithms and particle swarm optimization.