A discrete Consensus-Based Global Optimization Method with Noisy Objective Function

Stefania Bellavia () and Greta Malaspina ()
Additional contact information
Stefania Bellavia: Università degli Studi di Firenze
Greta Malaspina: Università degli Studi di Firenze

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 1, No 20, 40 pages

Abstract: Abstract Consensus based optimization is a derivative-free particles-based method for the solution of global optimization problems. Several versions of the method have been proposed in the literature, and different convergence results have been proved. However, all existing results assume the objective function to be evaluated exactly at each iteration of the method. In this work, we extend the convergence analysis of a discrete-time CBO method to the case where only a noisy stochastic estimator of the objective function can be computed at a given point. In particular we prove that under suitable assumptions on the oracle’s noise, the expected value of the mean squared distance of the particles from the solution can be made arbitrarily small in a finite number of iterations. Numerical experiments showing the impact of noise are also given.

Keywords: Global optimization; Consensus-based optimization; Noisy-functions; Subsampling; 65K10; 90C26; 90C56 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-025-02704-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:206:y:2025:i:1:d:10.1007_s10957-025-02704-6

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-025-02704-6

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().