Open Access
Issue
ESAIM: M2AN
Volume 55, Number 5, September-October 2021
Page(s) 1847 - 1871
DOI https://doi.org/10.1051/m2an/2021041
Published online 17 September 2021
  1. Y. Achdou, F. Camilli and I. Capuzzo-Dolcetta, Mean field games: numerical methods for the planning problem. SIAM J. Control Optim. 50 (2012) 77–109. [Google Scholar]
  2. M. Bardi and L.C. Evans, On hopf’s formulas for solutions of Hamilton-Jacobi equations. Nonlinear Anal.: Theory Methods App. 8 (1984) 1373–1381. [Google Scholar]
  3. J.-D. Benamou and Y. Brenier, A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numer. Math. 84 (2000) 375–393. [Google Scholar]
  4. J.-D. Benamou and G. Carlier, Augmented lagrangian methods for transport optimization, mean field games and degenerate elliptic equations. J. Optim. Theory App. 167 (2015) 1–26. [Google Scholar]
  5. J.-D. Benamou, G. Carlier and M. Laborde, An augmented lagrangian approach to wasserstein gradient flows and applications. ESAIM: Proce. Surv. 54 (2016) 1–17. [Google Scholar]
  6. M. Benzi, G. Golub and J. Liesen, Numerical solution of saddle point problems. Acta Numer. 14 (2005) 1–137. [Google Scholar]
  7. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge University Press (2004). [Google Scholar]
  8. C. Cancés, T. Gallouët and G. Todeschi, A variational finite volume scheme for wasserstein gradient flows. Numer. Math. 146 (2020) 437–480. [Google Scholar]
  9. J.A. Carrillo, K. Craig, L. Wang and C. Wei, Primal dual methods for wasserstein gradient flows. Found. Comput. Math. (2021). DOI: 10.1007/s10208-021-09503-1. [Google Scholar]
  10. C. Chainais-Hillairet, J.-G. Liu and Y.-J. Peng, Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis. Math. Modell. Numer. Anal. 37 (2003) 319–338. [Google Scholar]
  11. M. Erbar, M. Rumpf, B. Schmitzer and S. Simon, Computation of optimal transport on discrete metric measure spaces. Numer. Math. 144 (2020) 157–200. [Google Scholar]
  12. R. Eymard and G. Thierry, H-convergence and numerical schemes for elliptic problems. SIAM J. Numer. Anal. 41 (2003) 539–562. [Google Scholar]
  13. R. Eymard, T. Gallouët and R. Herbin, Finite volume methods. In: Vol. 7 of Handbook of Numerical Analysis (2000) 713–1020. [Google Scholar]
  14. R. Eymard, T. Gallouët and R. Herbin, Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes sushi: a scheme using stabilization and hybrid interfaces. IMA J. Numer. Anal. 30 (2009) 1009–1043. [Google Scholar]
  15. E. Facca, F. Cardin and M. Putti, Towards a stationary Monge-Kantorovich dynamics: the physarum polycephalum experience. SIAM J. Appl. Math. 78 (2018) 651–676. [Google Scholar]
  16. E. Facca, S. Daneri, F. Cardin and M. Putti, Numerical solution of Monge-Kantorovich equations via a dynamic formulation. J. Sci. Comput. 82 (2020) 1–26. [Google Scholar]
  17. A. Forsgren, P.E. Gill and M.H. Wright, Interior methods for nonlinear optimization. SIAM Rev. 44 (2002) 525–597. [Google Scholar]
  18. FVCAV, Benchmark. https://www.i2m.univ-amu.fr/fvca5/benchmark/Meshes/index.html. [Google Scholar]
  19. P. Gladbach, E. Kopfer and J. Maas, Scaling limits of discrete optimal transport. Preprint arXiv:1809.01092 (2018). [Google Scholar]
  20. J. Gondzio, Interior point methods 25 years later. Eur. J. Oper. Res. 218 (2012) 587–601. [Google Scholar]
  21. H. Lavenant, Unconditional convergence for discretizations of dynamical optimal transport. Preprint arXiv:1909.08790 (2019). [Google Scholar]
  22. H. Lavenant, S. Claici, E. Chien and J. Solomon, Dynamical optimal transport on discrete surfaces. ACM Trans. Graphics (TOG) 37 (2018) 1–16. [Google Scholar]
  23. W. Li, P. Yin and S. Osher, Computations of optimal transport distance with fisher information regularization. J. Sci. Comput. 75 (2018) 1581–1595. [Google Scholar]
  24. A. Natale and G. Todeschi, A mixed finite element discretization of dynamical optimal transport. Working paper or Preprint arXiv:2003.04558 (2020). [Google Scholar]
  25. A. Natale and G. Todeschi, TPFA finite volume approximation of Wasserstein gradient flows. In: Finite Volumes for Complex Applications IX – Methods, Theoretical Aspects, Examples. Springer International Publishing (2020) 193–201. [Google Scholar]
  26. N. Papadakis, G. Peyré and E. Oudet, Optimal transport with proximal splitting. SIAM J. Imaging Sci. 7 (2014) 212–238. [Google Scholar]
  27. I. Pòlik and T. Terlaky, Interior point methods for nonlinear optimization, edited by G. Di Pillo and F. Schoen. In: Nonlinear Optimization. Vol. 1989 of Lecture Notes in Mathematics. Springer Berlin Heidelberg (2010). [Google Scholar]
  28. F. Santambrogio, Optimal Transport for Applied Mathematicians. Birkäuser, NY (2015) 99–102. [Google Scholar]
  29. F. Santambrogio and X.-J. Wang, Convexity of the support of the displacement interpolation: counter examples. Appl. Math. Lett. 58 (2016) 152–158. [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.

Recommended for you