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Consensus-based optimization (CBO) is an agent-based derivative-free method for non-smooth global optimization that has been introduced in 2017, leveraging a surprising interplay between stochastic exploration and Laplace principle. In…

Analysis of PDEs · Mathematics 2024-10-01 Massimo Fornasier , Lukang Sun

In this paper, we are interested in finding the global minimizer of a nonsmooth nonconvex unconstrained optimization problem. By combining the discrete consensus-based optimization (CBO) algorithm and the gradient descent method, we develop…

Optimization and Control · Mathematics 2025-01-16 Jiazhen Wei , Fan Wu , Wei Bian

Introduced in 2017 \cite{B1-pinnau2017consensus}, Consensus-Based Optimization (CBO) has rapidly emerged as a significant breakthrough in global optimization. This straightforward yet powerful multi-particle, zero-order optimization method…

Analysis of PDEs · Mathematics 2025-05-29 Massimo Fornasier , Lukang Sun

We establish a uniform-in-time estimate for the mean-field convergence of the Consensus-Based Optimization (CBO) algorithm by rescaling the consensus point in the dynamics with a small parameter $\kappa \in (0,1)$. This uniform-in-time…

Optimization and Control · Mathematics 2025-07-01 Hui Huang , Hicham Kouhkouh

We analyze the Consensus-Based Optimization (CBO) algorithm with a consensus point rescaled by a small fixed parameter $\kappa \in (0,1)$. Under minimal assumptions on the objective function and the initial data, we establish its…

Optimization and Control · Mathematics 2026-01-19 Hui Huang , Hicham Kouhkouh , Lukang Sun

We study Consensus-Based Optimization (CBO) for two-layer neural network training. We compare the performance of CBO against Adam on two test cases and demonstrate how a hybrid approach, combining CBO with Adam, provides faster convergence…

Machine Learning · Computer Science 2025-12-03 William De Deyn , Michael Herty , Giovanni Samaey

In this paper, we propose a predictor-corrector type Consensus Based Optimization (CBO) algorithm on a convex feasible set. Our proposed algorithm generalizes the CBO algorithm in [11] to tackle a constrained optimization problem for the…

Optimization and Control · Mathematics 2021-10-14 Hyeong-Ohk Bae , Seung-Yeal Ha , Myeongju Kang , Hyuncheul Lim , Chanho Min , Jane Yoo

Consensus based optimization (CBO) employs a swarm of particles evolving as a system of stochastic differential equations (SDEs). Recently, it has been adapted to yield a derivative free sampling method referred to as consensus based…

Optimization and Control · Mathematics 2024-09-06 Marvin Koß , Simon Weissmann , Jakob Zech

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 non-convex functions in multiple dimensions. The feedback…

Optimization and Control · Mathematics 2025-07-29 Yuyang Huang , Michael Herty , Dante Kalise , Nikolas Kantas

Global optimization of a non-convex objective function often appears in large-scale machine-learning and artificial intelligence applications. Recently, consensus-based optimization (in short CBO) methods have been introduced as one of the…

Optimization and Control · Mathematics 2019-10-21 Seung-Yeal Ha , Shi Jin , Doheon Kim

In this work we are interested in the construction of numerical methods for high dimensional constrained nonlinear optimization problems by particle-based gradient-free techniques. A consensus-based optimization (CBO) approach combined with…

Optimization and Control · Mathematics 2021-11-23 Giacomo Borghi , Michael Herty , Lorenzo Pareschi

Consensus-based optimization (CBO) has established itself as an efficient gradient-free optimization scheme, with attractive mathematical properties, such as mean-field convergence results for non-convex loss functions. In this work, we…

Optimization and Control · Mathematics 2025-07-01 Tim Roith , Leon Bungert , Philipp Wacker

In this paper we propose a variant of a consensus-based global optimization (CBO) method that uses personal best information in order to compute the global minimum of a non-convex, locally Lipschitz continuous function. The proposed…

Optimization and Control · Mathematics 2020-08-25 Claudia Totzeck , Marie-Therese Wolfram

A self-interacting dynamics that mimics the standard Consensus-Based Optimization (CBO) model is introduced. This single-particle dynamics is shown to converge to a unique invariant measure that approximates the global minimum of a given…

Optimization and Control · Mathematics 2024-11-18 Hui Huang , Hicham Kouhkouh

In this paper, we propose consensus-based optimization for saddle point problems (CBO-SP), a novel multi-particle metaheuristic derivative-free optimization method capable of provably finding global Nash equilibria. Following the idea of…

Optimization and Control · Mathematics 2024-08-05 Hui Huang , Jinniao Qiu , Konstantin Riedl

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…

Optimization and Control · Mathematics 2021-11-05 J. A. Carrillo , C. Totzeck , U. Vaes

We present convergence and error estimates of the time-discrete consensus-based optimization(CBO) algorithms proposed in [arXiv:1909.09249] for general nonconvex functions. In authors' recent work [arxiv: 1910.08239], rigorous error…

Optimization and Control · Mathematics 2020-03-12 Seug-Yeal Ha , Shi Jin , Doheon Kim

In this paper, we introduce a novel variant of the CBO method that incorporates jumps according to an $\alpha$-stable stochastic process in a kinetic framework. This extension gives rise to nonlocal stochastic effects, which improve the…

Optimization and Control · Mathematics 2026-04-08 Pedro Aceves-Sanchez , Giacomo Albi , Federica Ferrarese , Michael Herty

Zero-order optimization has recently received significant attention for designing optimal trajectories and policies for robotic systems. However, most existing methods (e.g., MPPI, CEM, and CMA-ES) are local in nature, as they rely on…

Robotics · Computer Science 2026-02-09 Xudong Sun , Armand Jordana , Massimo Fornasier , Jalal Etesami , Majid Khadiv

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…

Optimization and Control · Mathematics 2025-04-04 Stefania Bellavia , Greta Malaspina