Open Access
Volume 52, Number 5, September–October 2018
Page(s) 2109 - 2132
Published online 25 January 2019
  1. L. Ambrosio, N. Gigli and G. Savaré, Gradient Flows in Metric Spaces and in the Space of Probability Measures. Lectures in Mathematics. ETH Zürich, Birkhäuser (2005). [Google Scholar]
  2. J.W. Barrett and L. Prigozhin, Partial 1 Monge–Kantorovich problem: variational formulation and numerical approximation. Interfaces Free Bound. 11 (2009) 201–238. [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 Appl. 167 (2015) 1–26. [Google Scholar]
  5. J.D. Benamou, G. Carlier, M. Cuturi, L. Nenna and G. Peyré, Iterative Bregman projections for regularized transportation problems. SIAM J. Sci. Comput. 37 (2015) A1111–A1138. [Google Scholar]
  6. J.D. Benamou, G. Carlier and R. Hatchi, A numerical solution to Monge’s problem with a Finsler distance cost. ESAIM: M2AN (2017) DOI:10.1051/m2an/2016077. [Google Scholar]
  7. J.D. Benamou, G. Carlier and F. Santambrogio, Variational Mean Field Games. Vol. 1 of Active Particles. Springer (2017) 141–171. [Google Scholar]
  8. G. Bouchitté, G. Buttazzo and P. Seppercher, Energy with respect to a measure and applications to low dimensional structures. Calc. Var. 5 (1997) 37–54. [Google Scholar]
  9. G. Bouchitté, G. Buttazzo and P. Seppecher, Shape optimization solutions via Monge–Kantorovich equation. C. R. Acad. Sci. Paris Sér. I Math. 324 (1997) 1185–1191. [Google Scholar]
  10. L.M. Briceno-Arias, D. Kalise and F.J. Silva, Proximal Methods for Stationary Mean Field Games with Local Couplings. SIAM J. Control Optim. 56 (2018) 801–836. [Google Scholar]
  11. L. Caffarelli and R.J. McCann, Free boundaries in optimal transport and Monge–Ampere obstacle problems. Ann. Math. 171 (2010) 673–730 [Google Scholar]
  12. P. Cannarsa and C. Sinestrari, Semiconcave Functions, Hamilton–Jacobi Equations, and Optimal Control. Vol. 58 of Progress Nonlin. Differ. Equ. Appl. Springer (2004). [Google Scholar]
  13. P. Cardaliaguet, Weak solutions for first order mean field games with local coupling. Vol. 11 of Analysis and Geometry in Control Theory and its Applications. Springer (2015) 111–158. [Google Scholar]
  14. P. Cardaliaguet and P.J. Graber, Mean field games systems of first order. ESAIM: COCV 21 (2015) 690–722. [EDP Sciences] [Google Scholar]
  15. P. Cardaliaguet, G. Carlier and B. Nazaret, Geodesics for a class of distances in the space of probability measures. Calc. Var. Partial Differ. Equ. 48 (2013) 395–420. [Google Scholar]
  16. P. Cardaliaguet, A.R. Mészáros and F. Santambrogio, First order mean field games with density constraints: pressure equals price. SIAM J. Control Optim. 54 (2016) 2672–709. [Google Scholar]
  17. S. Chen and E. Indrei, On the regularity of the free boundary in the optimal partial transport problem for general cost functions. J. Differ. Equ. 258 (2015) 2618–2632. [Google Scholar]
  18. L. Chizat, G. Peyré, B. Schmitzer and F.X. Vialard, Scaling Algorithms for Unbalanced Transport Problems. Preprint arXiv:1607.05816 (2016). [Google Scholar]
  19. G. Davila and Y.H. Kim, Dynamics of optimal partial transport. Calc. Var. Partial Differ. Equ. 55 (2016) 116. [Google Scholar]
  20. J. Eckstein and D.P. Bertsekas, On the Douglas–Rachford splitting method and the proximal point algorithm for maximal monotone operators. Math. Program. 55 (1992) 293–318. [Google Scholar]
  21. I. Ekeland and R. Teman, Convex analysis and variational problems, in Studies in Mathematics and Its Applications, North-Holland American Elsevier, New York (1976). [Google Scholar]
  22. L.C. Evans, Partial differential equations, 2nd edn. Vol. 19 of Graduate Studies in Mathematics. American Mathematical Society (2010). [Google Scholar]
  23. A. Figalli, The optimal partial transport problem. Arch. Ration. Mech. Anal. 195 (2010) 533–560. [Google Scholar]
  24. M. Fortin and R. Glowinski, Augmented Lagrangian methods: applications to the numerical solution of boundary-value problems. Vol. 15 of Studies in Mathematics and Its Applications. North-Holland (1983). [Google Scholar]
  25. R. Glowinski and P. Le Tallec, Augmented Lagrangian and operator-splitting methods in nonlinear mechanics. Vol. 9 of Studies in Applied and Numerical Mathematics. SIAM (1989). [Google Scholar]
  26. F. Hecht, New development in FreeFem++. J. Numer. Math. 20 (2012) 251–266. [Google Scholar]
  27. M. Huang, P.E. Caines and R.P. Malhamé, Large-population cost-coupled LQG problems with nonuniform agents: individual-mass behavior and decentralized ε-Nash equilibria. IEEE Trans. Automat. Control 52 (2007) 1560–1571. [Google Scholar]
  28. N. Igbida and V.T. Nguyen, Optimal partial mass transportation and obstacle Monge–Kantorovich equation. J. Differ. Equ. 264 (2018) 6380–6417. [Google Scholar]
  29. N. Igbida and V.T. Nguyen, Augmented Lagrangian method for optimal partial transportation. IMA J. Numer. Anal. 38 (2018) 156–183. [Google Scholar]
  30. E. Indrei, Free boundary regularity in the optimal partial transport problem. J. Funct. Anal. 264 (2013) 2497–2528. [Google Scholar]
  31. C. Jimenez, Dynamic formulation of optimal transport problems. J. Convex Anal. 15 (2008) 593–622. [Google Scholar]
  32. J.M. Lasry and P.L. Lions, Jeux à champ moyen I. Le cas stationnaire. C. R. Math. Acad. Sci. Paris 343 (2006) 619–625. [Google Scholar]
  33. J.M. Lasry and P.L. Lions, Jeux à champ moyen II. Horizon fini et controle optimal. C. R. Math. Acad. Sci. Paris 343 (2006) 679–684. [Google Scholar]
  34. J.M. Lasry and P.L. Lions, Mean field games. Jpn J. Math. 2 (2007) 229–260. [Google Scholar]
  35. B. Maury, A. Roudneff-Chupin and F. Santambrogio, A macroscopic crowd motion model of gradient flow type. Math. Models Methods Appl. Sci. 20 (2010) 1787–1821. [Google Scholar]
  36. A.R. Mészáros and F.J. Silva, A variational approach to second order mean field games with density constraints: the stationary case. J. Math. Pures Appl. 104 (2015) 1135–1159. [Google Scholar]
  37. A.R. Mészáros and F.J. Silva, On the variational formulation of some stationary second order mean field games systems. SIAM J. Math. Anal. 50 (2018) 1255–1277. [Google Scholar]
  38. G.D. Philippis, A.R. Mészáros, F. Santambrogio and B. Velichkov, BV estimates in optimal transportation and applications. Arch. Ration. Mech. Anal. 219 (2016) 829–860. [Google Scholar]
  39. W. Rudin, Real and Complex Analysis. McGraw-Hill Book Co., New York (1987). [Google Scholar]
  40. F. Santambrogio, A modest proposal for MFG with density constraints. Netw. Heterog. Media 7 (2012) 337–347. [Google Scholar]
  41. F. Santambrogio, Optimal Transport for Applied Mathematicians. Vol. 87 of Progress in Nonlinear Differential Equations and Their Applications. Birkhäuser (2015). [Google Scholar]
  42. C. Villani, Topics in Optimal Transportation. Vol. 58 of Graduate Studies in Mathematics. American Mathematical Society (2003). [Google Scholar]
  43. C. Villani, Optimal Transport, Old and New. Vol. 338 of Grundlehren des Mathematischen Wissenschaften (Fundamental Principles of Mathematical Sciences). Springer, New York (2009). [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