Self-interacting CBO: Existence, uniqueness, and long-time convergence

TL;DR

This paper introduces a self-interacting dynamics model that converges to the global minimum of a function, establishing its connection to existing consensus-based optimization methods and proving convergence properties.

Contribution

The paper presents a new self-interacting single-particle dynamics that guarantees convergence to a global minimum and links it to the CBO with Personal Best model.

Findings

Converges to a unique invariant measure approximating the global minimum.

Establishes a connection between the new dynamics and CBO with Personal Best.

Proves long-time convergence of the proposed model.

Abstract

A self-interacting dynamics that mimics the standard Consensus-Based Optimization (CBO) model is introduced. This single-particle dynamics is shown to converge to a unique invariant measure that approximates the global minimum of a given function. As an application, its connection to CBO with Personal Best introduced by C. Totzeck and M.-T. Wolfram (Math. Biosci. Eng., 2020) has been established.