New Results for Consensus Based Optimization

Michael Herty (RWTH Aachen University)

Abstract. We are interested in the construction of numerical methods for (constrained) very high-dimensional constrained nonlinear optimization problems by gradient free techniques appearing data assimilation problems as well as learning applications. Gradients are replaced by particle approximations and recently different methods have been proposed, e.g. consensus-based or swarm-based methods.  We discuss new results  on constrained and  parametric case as well as their corresponding mean field descriptions in the many particle  limit. Those allow to show convergence as well as the analysis of properties of the new algorithm. Several numerical examples, also in high dimensions, illustrate the theoretical findings as well as the performance of those methods.