Fast and robust consensus-based optimization via optimal feedback control
OA Location
Author(s)
Huang, yuyang
Herty, Michael
Kalise, Dante
Kantas, Nikolaos
Type
Journal Article
Abstract
We propose a variant of consensus-based optimization (CBO) algorithms, controlled-CBO, which introduces a feedback control term to improve convergence towards global minimizers of nonconvex functions in multiple dimensions. The feedback law is a gradient of a numerical approximation to the Hamilton–Jacobi–Bellman (HJB) equation, which serves as a proxy of the original objective function. Thus, the associated control signal furnishes gradient-like information to facilitate the identification of the global minimum without requiring derivative computation from the objective function itself. The proposed method exhibits significantly improved performance over standard CBO methods in numerical experiments, particularly in scenarios involving a limited number of particles, or where the initial particle ensemble is not well positioned with respect to the global minimum. At the same time, the modification keeps the algorithm amenable to theoretical analysis in the mean-field sense. The superior convergence rates are assessed experimentally.
Date Issued
2026-02-01
Date Acceptance
2025-08-01
Citation
SIAM Journal on Scientific Computing, 2026, 48 (1), pp.A74-A102
ISSN
1064-8275
Publisher
Society for Industrial and Applied Mathematics
Start Page
A74
End Page
A102
Journal / Book Title
SIAM Journal on Scientific Computing
Volume
48
Issue
1
Copyright Statement
Copyright © 2026 Society for Industrial and Applied Mathematics. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Publication Status
Published
Date Publish Online
2026-01-02