Nesterov acceleration for the Wasserstein minimization of displacement-convex free energies
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866913151867420672 |
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| author | Monmarché, Pierre |
| author_facet | Monmarché, Pierre |
| contents | We show that the mean-field underdamped Langevin process (associated to the non-linear Vlasov-Fokker-Planck equation) achieves a Nesterov acceleration with respect to the Wasserstein gradient flow of a displacement-convex free energy, in the sense that it converges at a rate of order given by the square-root of the Polyak-Łojasiewicz constant of the free energy (which is the optimal convergence rate for the corresponding gradient flow). This result has been made possible by the recent breakthrough [42] by Jianfeng Lu, which establishes such a \emph{diffusive-to-ballistic} improvement in term of entropy in the linear case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13186 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nesterov acceleration for the Wasserstein minimization of displacement-convex free energies Monmarché, Pierre Analysis of PDEs Optimization and Control Probability We show that the mean-field underdamped Langevin process (associated to the non-linear Vlasov-Fokker-Planck equation) achieves a Nesterov acceleration with respect to the Wasserstein gradient flow of a displacement-convex free energy, in the sense that it converges at a rate of order given by the square-root of the Polyak-Łojasiewicz constant of the free energy (which is the optimal convergence rate for the corresponding gradient flow). This result has been made possible by the recent breakthrough [42] by Jianfeng Lu, which establishes such a \emph{diffusive-to-ballistic} improvement in term of entropy in the linear case. |
| title | Nesterov acceleration for the Wasserstein minimization of displacement-convex free energies |
| topic | Analysis of PDEs Optimization and Control Probability |
| url | https://arxiv.org/abs/2605.13186 |