# Consensus-based Optimization and Ensemble Kalman Inversion for Global Optimization Problems with Constraints

arXiv: https://arxiv.org/abs/2111.02970 · HTML: https://mlsanity.com/paper/2111.02970/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Nov 2021.

## Built on by (most cited first, 3 of 3)

- [FedCBO: Reaching Group Consensus in Clustered Federated Learning through Consensus-based Optimization](https://mlsanity.com/paper/2305.02894/) (2023)
- [Consensus-based optimization for closed-box adversarial attacks and a connection to evolution strategies](https://mlsanity.com/paper/2506.24048/) (2025)
- [Non-intrusive surrogate modelling using sparse random features with applications in crashworthiness analysis](https://mlsanity.com/paper/2212.14507/) (2022)

## Abstract (arXiv)

We introduce a practical method for incorporating equality and inequality constraints in global optimization methods based on stochastic interacting particle systems, specifically consensus-based optimization (CBO) and ensemble Kalman inversion (EKI). Unlike other approaches in the literature, the method we propose does not constrain the dynamics to the feasible region of the state space at all times; the particles evolve in the full space, but are attracted towards the feasible set by means of a penalization term added to the objective function and, in the case of CBO, an additional relaxation drift. We study the properties of the method through the associated mean-field Fokker--Planck equation and demonstrate its performance in numerical experiments on several test problems.