An analytical framework for a consensus-based global optimization method

TL;DR

This paper introduces an analytical framework for a consensus-based global optimization method, demonstrating its convergence to the global minimum and validating it through theoretical analysis and numerical simulations.

Contribution

It provides the first mean-field convergence analysis for a consensus-based optimization algorithm, including variants with nonlinear diffusion.

Findings

Proves convergence to the global minimizer for a broad class of functions.

Validates theoretical results with numerical simulations.

Introduces variants of the method with nonlinear diffusion.

Abstract

In this paper we provide an analytical framework for investigating the efficiency of a consensus-based model for tackling global optimization problems. This work justifies the optimization algorithm in the mean-field sense showing the convergence to the global minimizer for a large class of functions. Theoretical results on consensus estimates are then illustrated by numerical simulations where variants of the method including nonlinear diffusion are introduced.