EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 32 (2026) ESAIM: COCV, 32 (2026) 24 References
Open Access
Issue
ESAIM: COCV
Volume 32, 2026
Article Number 24
Number of page(s) 48
DOI https://doi.org/10.1051/cocv/2026005
Published online 31 March 2026
  1. S. Kirkpatrick, C.D. Gelatt Jr. and M.P. Vecchi, Optimization by simulated annealing. Science 220 (1983) 671–680. [CrossRef] [MathSciNet] [Google Scholar]
  2. P.J.M. Van Laarhoven and E.H.L. Aarts, Simulated annealing: Theory and applications. Springer, Dordrecht, The Netherlands (1987). [Google Scholar]
  3. A. Dekkers and E. Aarts, Global optimization and simulated annealing. Math. Program. 50 (1991) 367–393. [Google Scholar]
  4. S. Geman and C.-R. Hwang, Diffusions for global optimization. SIAM J. Control Optim. 24 (1986) 1031–1043. [Google Scholar]
  5. T.-S. Chiang, C.-R. Hwang and S.J. Sheu, Diffusion for global optimization in ℝn. SIAM J. Control Optim. 25 (1987) 737–753. [Google Scholar]
  6. D.P. Bertsekas, Nonlinear Programming, 2nd edn. Athena Scientific, Belmont, MA, USA (1999). [Google Scholar]
  7. J. Nocedal and S.J. Wright, Numerical Optimization, 2nd edn. Springer, New York, NY, USA (2006). [Google Scholar]
  8. R.A. Holley, S. Kusuoka and D.W. Stroock, Asymptotics of the spectral gap with applications to the theory of simulated annealing. J. Funct. Anal. 83 (1989) 333–347. [CrossRef] [MathSciNet] [Google Scholar]
  9. C.-R. Hwang, Laplace's method revisited: weak convergence of probability measures. Ann. Probab. 8 (1980) 1177–1182. [Google Scholar]
  10. M. Hasenpflug, D. Rudolf and B. Sprungk, Wasserstein convergence rates of increasingly concentrating probability measures. Ann. Appl. Probab. 34 (2024) 3320–3347. [Google Scholar]
  11. D.W. Stroock and S.R. Srinivasa Varadhan, Multidimensional Diffusion Processes. Springer, Berlin, Heidelberg (2006). [Google Scholar]
  12. R.A. Holley and D.W. Stroock, Simulated annealing via Sobolev inequalities. Commun. Math. Phys. 115 (1988) 553–569. [Google Scholar]
  13. P. Monmarche, Piecewise deterministic simulated annealing. ALEA Latin Am. J. Probab. Math. Stat. 13 (2016) 357–398. [Google Scholar]
  14. L. Ambrosio, N. Gigli and G. Savare, Gradient Flows in Metric Spaces and in the Space of Probability Measures. Birkhäuser, 2nd ed., (2008). [Google Scholar]
  15. R. Jordan, D. Kinderlehrer and F. Otto, The variational formulation of the Fokker-Planck equation. SIAM J. Math. Anal. 29 (1998) 1–17. [Google Scholar]
  16. J. Bolte, L. Miclo and S. Villeneuve, Swarm gradient dynamics for global optimization: the mean-field limit case. Math. Program. 205 (2024) 661–701. [Google Scholar]
  17. P. Fearnhead, J. Bierkens, M. Pollock and G.O. Roberts, Piecewise deterministic Markov processes for continuous-time Monte Carlo. Stat. Sci. 33 (2018) 386–412. [Google Scholar]
  18. E. Zhou and X. Chen, Sequential Monte Carlo simulated annealing. J. Global Optim. 55 (2013) 101–124. [Google Scholar]
  19. Q. Liu and D. Wang, Stein variational gradient descent: a general purpose Bayesian inference algorithm. Adv. Neural Inform. Process. Syst. 29 (2016) 2378–2386. [Google Scholar]
  20. 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]
  21. A. Ringh and A. Sharma, Kalman–Langevin dynamics: exponential convergence, particle approximation and numerical approximation. arXiv preprint arXiv:2504.18139 (2025). [Google Scholar]
  22. J.A. Carrillo, Y.-P. Choi, C. Totzeck and O. Tse, An analytical framework for consensus-based global optimization method. Math. Models Methods Appi. Sci. 28 (2018) 1037–1066. [Google Scholar]
  23. J.A. Carrillo, F. Hoffmann, A.M. Stuart and U. Vaes, Consensus-based sampling. Stud. Appl. Math. 148 (2022) 1069–1140. [Google Scholar]
  24. 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]
  25. J. Heng, A. Doucet and Y. Pokern, Gibbs flow for approximate transport with applications to Bayesian computation. J. Roy. Stat. Soc. B: Stat. Methodol. 83 (2021) 156–187. [Google Scholar]
  26. Y. Tian, N. Panda and Y.T. Lin. Liouville Flow Importance Sampler. Proceedings of the 41st International Conference on Machine Learning in Proceedings of Machine Learning Research 235 (2024) 48186–48210. [Google Scholar]
  27. F. Vargas, S. Padhy, D. Blessing and N. Nüsken, Transport meets variational inference: Controlled Monte Carlo Diffusions, in International Conference on Representation Learning, vol. 2024, edited by B. Kim, Y. Yue, S. Chaudhuri, K. Fragkiadaki, M. Khan and Y. Sun (2024) 55236–55278. [Google Scholar]
  28. M.S. Albergo and E. Vanden-Eijnden, Nets: a non-equilibrium transport sampler. Michael Samuel Albergo, Eric Vanden-Eijnden Proceedings of the 42nd International Conference on Machine Learning, PMLR 267 (2025) 1026–1055. [Google Scholar]
  29. S. Vaikuntanathan and C. Jarzynski, Escorted free energy simulations: improving convergence by reducing dissipation. Phys. Rev. Lett. 100 (2008) 190601. [Google Scholar]
  30. S. Reich, A nonparametric ensemble transform method for Bayesian inference. SIAM J. Sci. Comput. 35 (2013) A2013-A2024. [Google Scholar]
  31. M.D. Parno and Y.M. Marzouk, Transport map accelerated Markov chain Monte Carlo. SIAM/ASA J. Uncertainty Quantif. 6 (2018) 645–682. [Google Scholar]
  32. Y. Chen, T.T. Georgiou and M. Pavon, Stochastic control liaisons: Richard Sinkhorn meets Gaspard Monge on a Schrödinger bridge. SIAM Rev. 63 (2021) 249–313. [Google Scholar]
  33. M. Schauer, F. van der Meulen and H. van Zanten, Guided proposals for simulating multi-dimensional diffusion bridges. Bernoulli 23 (2017) 2917–2950. [Google Scholar]
  34. M. Corstanje, F. van der Meulen and M. Schauer, Conditioning continuous-time Markov processes by guiding. Stochastics 95 (2023) 963–996. [Google Scholar]
  35. E. Bernton, J. Heng, A. Doucet and P.E Jacob, Schrödinger bridge samplers. arXiv preprint arXiv:1912.13170 (2019). [Google Scholar]
  36. A. Forsgren, P.E. Gill and M.H. Wright, Interior methods for nonlinear optimization. SIAM Rev. 44 (2002) 525–597. [Google Scholar]
  37. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge University Press, Cambridge, UK (2004). [Google Scholar]
  38. R.J. Vanderbei, Linear Programming, 3rd edn. Springer, Cham, Switzerland (2008). [Google Scholar]
  39. E.H. Lieb and M. Loss, Analysis, 2nd edn. American Mathematical Society, Providence, RI, USA (2001). [Google Scholar]
  40. C. Villani, Optimal Transport: Old and New. Springer Berlin Heidelberg (2008). [Google Scholar]
  41. C. Villani, Topics in Optimal Transportation. American Mathematical Society, Providence, RI, USA (2003). [Google Scholar]
  42. D.C. Dowson and B.V. Landau. The Fréchet distance between multivariate normal distributions. J. Multivariate Anal. 12 (1982) 450–455. [Google Scholar]
  43. C.R. Givens and R.M. Shortt, A class of Wasserstein metrics for probability distributions. Michigan Math. J. 31 (1984) 231–240. [CrossRef] [MathSciNet] [Google Scholar]
  44. M. Knott and C.S. Smith, On the optimal mapping of distributions. J. Optim. Theory Appl. 43 (1984) 39–49. [Google Scholar]
  45. G. Peyré and M. Cuturi, Computational optimal transport: With applications to data science. Found. Trends Mach. Learn. 11 (2019) 355–607. [CrossRef] [Google Scholar]
  46. A. Kazeykina, Z. Ren, X. Tan and J. Yang, Ergodicity of the underdamped mean-field Langevin dynamics. Ann. Appl. Probab. 34 (2024) 3181–3226. [Google Scholar]
  47. D. Bakry, F. Barthe, P. Cattiaux and A. Guillin, A simple proof of the Poincaré inequality for a large class of probability measures. Electron. Commun. Probab. 13 (2008) 60–66. [Google Scholar]
  48. D.G. Luenberger, Optimization by Vector Space Methods. John Wiley & Sons, Inc., New York, NY, USA (1969). [Google Scholar]
  49. G. Menz and A. Schlichting, Poincaré and lorarithmic Sobolev inequalities by decomposition of the energy landscape. Ann. Probab. 42 (2014) 1809–1884. [CrossRef] [MathSciNet] [Google Scholar]
  50. O. Kallenberg, Foundations of Modern Probability, 3rd edn. Springer (2021). [Google Scholar]
  51. L.C.G. Rogers and D. Williams, Diffusions, Markov Processes and Martingales: Itô Calculus, Vol. 2. Cambridge University Press, Cambridge, UK (2000). [Google Scholar]
  52. V.I. Bogachev, N.V. Krylov, M. Röckner and S.V. Shaposhnikov, Fokker–Planck–Kolmogorov Equations. American Mathematical Society, Providence, RI, USA (2022). [Google Scholar]
  53. E.A.J.F. Peters and G. de With, Rejection-free Monte Carlo sampling for general potentials. Phys. Rev. E 85 (2012) 026703. [CrossRef] [PubMed] [Google Scholar]
  54. A. Bouchard-Côté, S.J. Vollmer and A. Doucet, The bouncy particle sampler: a nonreversible rejection-free Markov chain Monte Carlo method. J. Am. Stat. Assoc. 113 (2018) 855–867. [Google Scholar]
  55. M.H.A. Davis, Markov Models & Optimization. Chapman & Hall, Boca Raton, FL, USA (1993). [Google Scholar]
  56. P. Holderrieth, Cores for piecewise-deterministic Markov processes used in Markov chain Monte Carlo. Electron. Commun. Probab. 26 (2021) 1–12. [Google Scholar]
  57. H. Kunita, Stochastic Flows and Stochastic Differential Equations. Cambridge University Press (1990). [Google Scholar]
  58. F. Baudoin, Diffusion Processes and Stochastic Calculus. European Mathematical Society (2014). [Google Scholar]
  59. C.-R. Hwang, Frozen Patterns and Minimal Energy States. PhD thesis, Brown University (1978). [Google Scholar]
  60. C.P. Robert and G. Casella, Monte Carlo Statistical Methods. Springer, New York, NY, USA (2004). [Google Scholar]
  61. N. Bonneel, M. Van De Panne, S. Paris and W. Heidrich, Displacement interpolation using Lagrangian mass transport, in Proceedings of the 2011 SIGGRAPH Asia Conference (2011) 1–12. [Google Scholar]
  62. M. Cuturi, Sinkhorn distances: lightspeed computation of optimal transport. Adv. Neural Inform. Process. Syst. 26 (2013) 2292–2300. [Google Scholar]
  63. A.-A. Pooladian and J. Niles-Weed, Entropic estimation of optimal transport maps. arXiv preprint arXiv:2109.12004 (2021). [Google Scholar]
  64. S. Mehrotra, On the implementation of a primal-dual interior point method. SIAM J. Optim. 2 (1992) 575–601. [Google Scholar]
  65. S. Mizuno, M.J. Todd and Y. Ye, On adaptive-step primal-dual interior-point algorithms for linear programming. Math. Oper. Res. 18 (1993) 964–981. [Google Scholar]
  66. T. Guilmeau, E. Chouzenoux and V. Elvira, Simulated annealing: a review and a new scheme, in 2021 IEEE Statistical Signal Processing Workshop (SSP). IEEE (2021) 101–105. [Google Scholar]
  67. T. Akiba, S. Sano, T. Yanase, T. Ohta and M. Koyama, Optuna: a next-generation hyperparameter optimization framework, in Proceedings of the 25th A CM SIGKDD International Conference on Knowledge Discovery and Data Mining (2019). [Google Scholar]
  68. P. Kidger, On Neural Differential Equations. PhD thesis, University of Boxford (2021). [Google Scholar]
  69. J. Bradbury, R. Frostig, P. Hawkins, M.J. Johnson, C. Leary, D. Maclaurin, G. Necula, A. Paszke, J. VanderPlas, S. Wanderman-Milne and Q. Zhang, JAX: composable transformations of Python+NumPy programs (2018). [Google Scholar]
  70. V. Molin, Code for "Controlled stochastic processes for simulated annealing". https://github.com/vincentmolin/controlled_annealing (2025). [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.