Consensus based optimization via jump-diffusion stochastic differential equations
Author(s)
Kalise, Dante
Sharma, Akash
Tretyakov, Michael
Type
Journal Article
Abstract
We introduce a new consensus-based optimization (CBO) method where an interacting particle system is driven by jump-diffusion stochastic differential equations (SDEs). We study well-posedness of the particle system as well as of its mean-field limit. The major contributions of this paper are proofs of convergence of the interacting particle system towards the mean-field limit and convergence of a discretized particle system towards the continuous-time dynamics in the mean-square sense. We also prove convergence of the mean-field jump-diffusion SDEs towards global minimizer for a large class of objective functions. We demonstrate improved performance of the proposed CBO method over earlier CBO methods in numerical simulations on benchmark objective functions.
Date Issued
2023-02-01
Date Acceptance
2022-12-14
Citation
Mathematical Models and Methods in Applied Sciences (M3AS), 2023, 33 (02), pp.289-339
ISSN
0218-2025
Publisher
World Scientific Publishing
Start Page
289
End Page
339
Journal / Book Title
Mathematical Models and Methods in Applied Sciences (M3AS)
Volume
33
Issue
02
Copyright Statement
© 2023 World Scientific Publishing.
Publication Status
Published