An analytical framework for consensus-based global optimization method

José A. Carrillo; Young Pil Choi; Claudia Totzeck; Oliver Tse

doi:10.1142/S0218202518500276

An analytical framework for consensus-based global optimization method

José A. Carrillo, Young Pil Choi, Claudia Totzeck, Oliver Tse

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

55 Citations (Scopus)

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.

Original language	English
Article number	00276
Journal	Mathematical Models and Methods in Applied Sciences
Volume	28
Issue number	6
DOIs	https://doi.org/10.1142/S0218202518500276
Publication status	Published - 2018 Jun 15

Bibliographical note

Funding 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.

Publisher Copyright:
© 2018 World Scientific Publishing Company.

All Science Journal Classification (ASJC) codes

Modelling and Simulation
Applied Mathematics

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10.1142/S0218202518500276

Cite this

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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.",

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An analytical framework for consensus-based global optimization method

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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