EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 31 (2025) ESAIM: COCV, 31 (2025) 74 References
Open Access
Issue
ESAIM: COCV
Volume 31, 2025
Article Number 74
Number of page(s) 44
DOI https://doi.org/10.1051/cocv/2025060
Published online 29 August 2025
  1. R. Pinnau, C. Totzeck, O. Tse and S. Martin, A consensus-based model for global optimization and its mean-field limit. Math. Models Methods Appl. Sci. 27 (2017) 183–204. [CrossRef] [MathSciNet] [Google Scholar]
  2. J.A. Carrillo, F. Hoffmann, A.M. Stuart and U. Vaes, Consensus-based sampling. Stud. Appl. Math. 148 (2022) 1069–1140. [Google Scholar]
  3. R.E. James Kennedy, The particle swarm: social adaptation of knowledge. Proceedings of ICNN’95 – International Conference on Neural Networks (1995) 1942–1948. [Google Scholar]
  4. J. Kennedy, The particle swarm: social adaptation of knowledge. Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC ’97) (1997) 303–308. [Google Scholar]
  5. C. Totzeck, R. Pinnau, S. Blauth and S. Schotthöfer, A numerical comparison of consensus-based global optimization to other particle-based global optimization schemes. PAMM 18 (2018) e201800291. [Google Scholar]
  6. J.A. Carrillo, S. Jin, L. Li and Y. Zhu, A consensus-based global optimization method for high dimensional machine learning problems. ESAIM COCV. 27 (2021) S5. [Google Scholar]
  7. M. Fornasier, H. Huang, L. Pareschi and P. Sünnen, Consensus-based optimization on the sphere: convergence to global minimizers and machine learning. J. Mach. Learn. Res. 22 (2021). Paper No. 237, 55. [Google Scholar]
  8. S. Grassi and L. Pareschi, From particle swarm optimization to consensus based optimization: stochastic modeling and mean-field limit. Math. Models Methods Appl. Sci. 31 (2021) 1625–1657. [CrossRef] [MathSciNet] [Google Scholar]
  9. S. Grassi, H. Huang, L. Pareschi and J. Qiu, Mean-field particle swarm optimization, in Modeling and Simulation for Collective Dynamics. World Scientific (2023) 127–193. [Google Scholar]
  10. H. Huang, J. Qiu and K. Riedl, On the global convergence of particle swarm optimization methods. Appl. Math. Optim. 88 (2023) 30. [Google Scholar]
  11. H.-O. Bae, S.-Y. Ha, M. Kang, H. Lim, C. Min and J. Yoo, A constrained consensus based optimization algorithm and its application to finance. Appl. Math. Comput. 416 (2022). Paper No. 126726, 10. [Google Scholar]
  12. K. Althaus, I. Papaioannou and E. Ullmann, Consensus-based rare event estimation. SIAM J. Sci. Comput. 46 (2024) A1487–A1513. [Google Scholar]
  13. J.A. Carrillo, N.G. Trillos, S. Li and Y. Zhu, FedCBO: Reaching group consensus in clustered federated learning through consensus-based optimization (2023). [Google Scholar]
  14. J.A. Carrillo, Y.-P. Choi, C. Totzeck and O. Tse, An analytical framework for consensus-based global optimization method. Math. Models Methods Appl. Sci. 28 (2016) 1037–1066. [Google Scholar]
  15. M. Fornasier, T. Klock and K. Riedl, Consensus-based optimization methods converge globally. SIAM J. Optim. 34 (2024) 2973–3004. [Google Scholar]
  16. J. Kennedy and R. Eberhart, Particle swarm optimization, in Proceedings of ICNN’95-International Conference on Neural Networks, vol. 4. IEEE (1995) 1942–1948. [Google Scholar]
  17. H. Huang and J. Qiu, On the mean-field limit for the consensus-based optimization. Math. Methods Appl. Sci. 45 (2022) 7814–7831. [Google Scholar]
  18. S.-Y. Ha, S. Jin and D. Kim, Convergence of a first-order consensus-based global optimization algorithm. Math. Models Methods Appl. Sci. 30 (2020) 2417–2444. [Google Scholar]
  19. S.-Y. Ha, M. Kang, D. Kim, J. Kim and I. Yang, Convergence and error estimates for time-discrete consensus-based optimization algorithms. Numer. Math. 147 (2021) 255–282. [Google Scholar]
  20. D. Ko, S.Y. Ha, S. Jin and D. Kim, Convergence analysis of the discrete consensus-based optimization algorithm with random batch interactions and heterogeneous noises. Math. Models Methods Appl. Sci. 32 (2022) 1071–1107. [Google Scholar]
  21. S. Jin, L. Li and J.-G. Liu, Random batch methods (RBM) for interacting particle systems. J. Comput. Phys. 400 (2020). 108877, 30. [CrossRef] [MathSciNet] [Google Scholar]
  22. C. Totzeck and M.-T. Wolfram, Consensus-based global optimization with personal best. Math. Biosci. Eng. 17 (2020) 6026–6044. [CrossRef] [MathSciNet] [Google Scholar]
  23. D. Kalise, A. Sharma and M.V. Tretyakov, Consensus-based optimization via jump-diffusion stochastic differential equations. Math. Models Methods Appl. Sci. 33 (2023) 289–339. [Google Scholar]
  24. K. Klamroth, M. Stiglmayr and C. Totzeck, Consensus-based optimization for multi-objective problems: a multiswarm approach. J. Glob. Optim. 89 (2024) 745–776. [Google Scholar]
  25. G. Borghi, M. Herty and L. Pareschi, An adaptive consensus based method for multi-objective optimization with uniform Pareto front approximation. Appl. Math. Optim. 88 (2023). Paper No. 58. [Google Scholar]
  26. M. Fornasier, H. Huang, L. Pareschi and P. Sünnen, Anisotropic diffusion in consensus-based optimization on the sphere. SIAM J. Optim. 32 (2022) 1984–2012. [Google Scholar]
  27. G. Borghi, M. Herty and L. Pareschi, Constrained consensus-based optimization. SIAM J. Optim. 33 (2023) 211–236. eprint: https://doi.org/10.1137/22M1471304. [Google Scholar]
  28. J.A. Carrillo, S. Jin, H. Zhang and Y. Zhu, An interacting particle consensus method for constrained global optimization. arXiv preprint arXiv:2405.00891 (2024). [Google Scholar]
  29. J.A. Carrillo, C. Totzeck and U. Vaes, Consensus-based Optimization and Ensemble Kalman Inversion for Global Optimization Problems with Constraints (2021) 195–230. [Google Scholar]
  30. J. Beddrich, E. Chenchene, M. Fornasier, H. Huang and B. Wohlmuth, Constrained consensus-based optimization and numerical heuristics for the few particle regime. arXiv preprint arXiv:2410.10361 (2024). [Google Scholar]
  31. M. Fornasier, H. Huang, L. Pareschi and P. Sünnen, Consensus-based optimization on hypersurfaces: well-posedness and mean-field limit. Math. Models Methods Appl. Sci. 30 (2020) 2725–2751. [Google Scholar]
  32. L. Bungert, T. Roith and P. Wacker, Polarized consensus-based dynamics for optimization and sampling. Math. Program. 211 (2025) 125–155. [Google Scholar]
  33. C. Cipriani, H. Huang and J. Qiu, Zero-inertia limit: from particle swarm optimization to consensus-based optimization. SIAM J. Math. Anal. 54 (2022) 3091–3121. [Google Scholar]
  34. C. Totzeck, Trends in consensus-based optimization, in Active particles. Vol. 3. Advances in Theory, Models, and Applications. Model. Simul. Sci. Eng. Technol. Birkhäuser/Springer, Cham (2022) 201–226. [Google Scholar]
  35. R. Bailo, A. Barbaro, S.N. Gomes, K. Riedl, T. Roith, C. Totzeck and U. Vaes, CBX: Python and Julia packages for consensus-based interacting particle methods. J. Open Source Softw. 9 (2024) 6611. [Google Scholar]
  36. A. Garbuno-Inigo, F. Hoffmann, W. Li and A.M. Stuart, Interacting Langevin diffusions: gradient structure and ensemble Kalman sampler. SIAM J. Appl. Dyn. Syst. 19 (2020) 412–441. [Google Scholar]
  37. B. Sprungk, S. Weissmann and J. Zech, Metropolis-adjusted interacting particle sampling. Stat. Comput. 35 (2025) 64. [Google Scholar]
  38. L.-P. Chaintron and A. Diez, Propagation of chaos: a review of models, methods and applications. II. Applications. Kinet. Relat. Models 15 (2022) 1017–1173. [Google Scholar]
  39. S. Agapiou, O. Papaspiliopoulos, D. Sanz-Alonso and A.M. Stuart, Importance sampling: intrinsic dimension and computational cost. Statist. Sci. 32 (2017) 405–431. [Google Scholar]
  40. P. Doukhan and G. Lang, Evaluation for moments of a ratio with application to regression estimation. Bernoulli 15 (2009) 1259–1286. [Google Scholar]
  41. M. Koß, S. Weissmann and J. Zech, On the mean field limit of consensus based methods. arXiv preprint, arXiv:2409.03518 (2024). [Google Scholar]
  42. D.J. Higham, X. Mao and A.M. Stuart, Strong convergence of Euler-type methods for nonlinear stochastic differential equations. SIAM J. Numer. Anal. 40 (2002) 1041–1063. [CrossRef] [MathSciNet] [Google Scholar]
  43. M. Mitzenmacher and E. Upfal, Probability and Computing, 2nd edn. Cambridge University Press, Cambridge (2017). Randomization and probabilistic techniques in algorithms and data analysis. [Google Scholar]
  44. L.-P. Chaintron and A. Diez, Propagation of chaos: a review of models, methods and applications. I. Models and methods. Kinet. Relat. Models 15 (2022) 895–1015. 15(6):895-1015, 2022. [CrossRef] [MathSciNet] [Google Scholar]
  45. X. Mao, Stochastic Differential Equations and Applications, 2nd edn. Horwood Publishing Limited, Chichester (2008). [Google Scholar]
  46. C. Villani, Optimal Transport. Vol. 338 of Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin (2009). [Google Scholar]
  47. C. Villani, Topics in Optimal Transportation. Vol. 58 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI (2003). [Google Scholar]
  48. H. Araki and S. Yamagami, An inequality for Hilbert–Schmidt norm. Commun. Math. Phys. 81 (1991) 89–96. [Google Scholar]
  49. F. Kittaneh, On Lipschitz functions of normal operators. Proc. Amer. Math. Soc. 94 (1985) 416–418. [Google Scholar]
  50. R. Bhatia, Matrix Factorizations and their Perturbations, vol. 197/198 (1994) 245–276. Second Conference of the International Linear Algebra Society (Lisbon, 1992). [Google Scholar]
  51. R. Bhatia, Matrix analysis. Vol. 169 of Graduate Texts in Mathematics. Springer-Verlag, New York (1997). [Google Scholar]
  52. R. Khasminskii, Stochastic Stability of Differential Equations. Vol. 66 of Stochastic Modelling and Applied Probability, 2nd edn. Springer, Heidelberg (2012). With contributions by G.N. Milstein and M.B. Nevelson. [Google Scholar]
  53. B. Øksendal, Stochastic Differential Equations, 6th edn. Universitext. Springer-Verlag, Berlin (2003). An introduction with applications. [Google Scholar]
  54. D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order. Classics in Mathematics. Springer-Verlag, Berlin (2001). Reprint of the 1998 edition. [Google Scholar]
  55. J.L. van Hemmen and T. Ando, An inequality for trace ideals. Commun. Math. Phys. 76 (1980) 143–148. [Google Scholar]
  56. A. Friedman, Stochastic differential equations and applications, in Stochastic Differential Equations. Vol. 77 of C.I.M.E. Summer School. Springer, Heidelberg (2010) 75–148. [Google Scholar]
  57. U. Vaes, Sharp propagation of chaos for the ensemble Langevin sampler. J. London Math. Soc. 110 (2024) e13008. [Google Scholar]
  58. A. Garbuno-Inigo, N. Nüsken and S. Reich, Affine invariant interacting Langevin dynamics for Bayesian inference. SIAM J. Appl. Dyn. Syst. 19 (2020) 1633–1658. [Google Scholar]
  59. S.N. Ethier and T.G. Kurtz, Markov Processes. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. John Wiley & Sons, Inc., New York (1986). Characterization and convergence. [Google Scholar]
  60. M.H. Duong and H.D. Nguyen, Asymptotic analysis for the generalized Langevin equation with singular potentials. J. Nonlinear Sci. 34 (2024). Paper No. 62, 63. [Google Scholar]
  61. M. Fornasier, T. Klock and K. Riedl, Convergence of anisotropic consensus-based optimization in mean-field Law, in Applications of Evolutionary Computation, edited by J.L. Jiménez Laredo, J. Ignacio Hidalgo and K.O. Babaagba. Springer International Publishing, Cham (2022) 738–754. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.