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Consensus-based optimization (CBO) is a versatile multi-particle optimization method for performing nonconvex and nonsmooth global optimizations in high dimensions. Proofs of global convergence in probability have been achieved for a broad…

Optimization and Control · Mathematics 2026-01-13 Jonas Beddrich , Enis Chenchene , Massimo Fornasier , Hui Huang , Barbara Wohlmuth

In this paper, we study consensus-based optimization (CBO), which is a multi-agent metaheuristic derivative-free optimization method that can globally minimize nonconvex nonsmooth functions and is amenable to theoretical analysis. Based on…

Numerical Analysis · Mathematics 2024-09-10 Massimo Fornasier , Timo Klock , Konstantin Riedl

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

Consensus-based optimization (CBO) is a powerful and versatile zero-order multi-particle method designed to provably solve high-dimensional global optimization problems, including those that are genuinely nonconvex or nonsmooth. The method…

Optimization and Control · Mathematics 2026-02-13 Massimo Fornasier , Hui Huang , Jona Klemenc , Greta Malaspina

This paper introduces an interacting-particle optimization method tailored to possibly non-convex composite optimization problems, which arise widely in signal processing. The proposed method, \emph{ProxiCBO}, integrates consensus-based…

Optimization and Control · Mathematics 2026-04-20 Haoyu Zhang , Yanting Ma , Ruangrawee Kitichotkul , Joshua Rapp , Petros Boufounos

In this paper we study consensus-based optimization (CBO), a versatile, flexible and customizable optimization method suitable for performing nonconvex and nonsmooth global optimizations in high dimensions. CBO is a multi-particle…

Numerical Analysis · Mathematics 2026-05-28 Konstantin Riedl

Consensus-based optimization (CBO) is a versatile multi-particle metaheuristic optimization method suitable for performing nonconvex and nonsmooth global optimizations in high dimensions. It has proven effective in various applications…

Optimization and Control · Mathematics 2026-05-12 Massimo Fornasier , Peter Richtárik , Konstantin Riedl , Lukang Sun

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

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

We analyze a zeroth-order particle algorithm for the global optimization of a non-convex function, focusing on a variant of Consensus-Based Optimization (CBO) with small but fixed noise intensity. Unlike most previous studies restricted to…

Optimization and Control · Mathematics 2025-11-24 Pascal Bianchi , Radu-Alexandru Dragomir , Victor Priser

In this work we propose MirrorCBO, a consensus-based optimization (CBO) method which generalizes standard CBO in the same way that mirror descent generalizes gradient descent. For this we apply the CBO methodology to a swarm of dual…

Optimization and Control · Mathematics 2025-07-17 Leon Bungert , Franca Hoffmann , Dohyeon Kim , Tim Roith

Consensus-based optimization (CBO) is a multi-agent metaheuristic derivative-free optimization algorithm that has proven to be capable of globally minimizing nonconvex nonsmooth functions across a diverse range of applications while being…

Optimization and Control · Mathematics 2025-12-12 Sabrina Bonandin , Konstantin Riedl , Sara Veneruso

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 novel multiscale consensus-based optimization (CBO) algorithm for solving bi- and tri-level optimization problems is introduced. Existing CBO techniques are generalized by the proposed method through the employment of multiple interacting…

Optimization and Control · Mathematics 2025-06-23 Michael Herty , Yuyang Huang , Dante Kalise , Hicham Kouhkouh

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

Lately, a novel swarm intelligence model, namely the consensus-based optimization (CBO) algorithm, was introduced to deal with the global optimization problems. Limited by the conditions of Ito's formula, the convergence analysis of the…

Optimization and Control · Mathematics 2025-01-14 Jiazhen Wei , Wei Bian

In this paper we study anisotropic consensus-based optimization (CBO), a multi-agent metaheuristic derivative-free optimization method capable of globally minimizing nonconvex and nonsmooth functions in high dimensions. CBO is based on…

Numerical Analysis · Mathematics 2024-03-26 Massimo Fornasier , Timo Klock , Konstantin Riedl

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

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

We propose Discrete Consensus-Based Optimization (DCBO), a fully discrete version of the Consensus-Based Optimization (CBO) framework. DCBO is a multi-agent method for the global optimization of possibly non-convex and non-differentiable…

Optimization and Control · Mathematics 2024-04-17 Junhyeok Byeon , Seung-Yeal Ha , Joong-Ho Won
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