An interacting particle consensus method for constrained global optimization
Optimization and Control
2026-03-31 v8 Numerical Analysis
Analysis of PDEs
Numerical Analysis
Abstract
This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed method combines components from consensus-based optimization algorithm with a newly introduced forcing term directed at the constraint set. A rigorous mean-field limit of the particle system is derived, and the convergence of the mean-field limit to the constrained minimizer is established. Additionally, we introduce a stable discretized algorithm and conduct various numerical experiments to demonstrate the performance of the proposed method.
Cite
@article{arxiv.2405.00891,
title = {An interacting particle consensus method for constrained global optimization},
author = {José A. Carrillo and Shi Jin and Haoyu Zhang and Yuhua Zhu},
journal= {arXiv preprint arXiv:2405.00891},
year = {2026}
}