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.
|Journal||Mathematical Models and Methods in Applied Sciences|
|Publication status||Published - 2018 Jun 15|
Bibliographical noteFunding Information:
JAC was partially supported by the Royal Society by a Wolfson Research Merit Award and by EPSRC Grant Number EP/P031587/1. Y-PC was supported by the Alexander Humboldt Foundation through the Humboldt Research Fellowship for Postdoctoral Researchers. Y-PC was also supported by NRF Grants (NRF-2017R1C1B2012918 and 2017R1A4A1014735). CT was partially supported by a “Kurzstipendium für Doktorandinnen und Doktoranden” by the German Academic Exchange Service. OT is thankful to Jim Portegies for stimulating discussions.
All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Applied Mathematics