| [1] |
Jean-David Benamou, Adam Oberman, and Froese Britanny. Numerical solution of the second boundary value problem for the Elliptic Monge-Ampère equation. Research report, INRIA, June 2012. [ bib | http | .pdf ]
Keywords: Optimal Transportation ; Monge-Ampére Equation
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| [2] |
Guillaume Carlier and Lina Mallozzi. Optimal monopoly pricing with congestion and random utility via partial mass transport. working paper or preprint, December 2016. [ bib | http | .pdf ]
Keywords: monopoly spatial pricing ; partial optimal mass transport ; congestion ; random utility
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| [3] |
Alpár Richárd Mészáros and Filippo Santambrogio. ADVECTION-DIFFUSION EQUATIONS WITH DENSITY CONSTRAINTS. Analysis and PDEs, 2016. [ bib | http | .pdf ]
Keywords: crowd motion ; Wasserstein space ; entropy ; Fokker-Planck
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| [4] |
Hugo Lavenant. Time-convexity of the entropy in the multiphasic formulation of the incompressible euler equation. working paper or preprint, 2017. [ bib | http | .pdf ]
Keywords: Flow interchange ; Euler equations ; Wasserstein space
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| [5] |
Yann Brenier. The initial value problem for the Euler equations of incompressible fluids viewed as a concave maximization problem . working paper or preprint, June 2017. [ bib | http | .pdf ]
Keywords: Fluid mechanics ; partial differential equations ; calculus of variation ; optimal transport ; Euler equations
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| [6] |
Yann Brenier. Connections between Optimal Transport, Combinatorial Optimization and Hydrodynamics. working paper or preprint, October 2014. [ bib | http | .pdf ]
Keywords: Optimal transport ; PDEs of Fluid Mechanics ; Calculus of Variations ; Combinatorial Optimization
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| [7] |
Giuseppe Buttazzo, Guillaume Carlier, and Serena Guarino Lo Bianco. Optimal regions for congested transport. working paper or preprint, 2014. [ bib | http | .pdf ] |
| [8] |
Filippo Santambrogio. A Dacorogna-Moser approach to flow decomposition and minimal flow problems. submitted to the proceedings of the SMAI conference 2013, October 2013. [ bib | http | .pdf ]
Keywords: normal currents ; cycles ; optimal transport
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| [9] |
F Al Reda and B Maury. Interpretation of Finite Volume discretization schemes for the Fokker Planck equation as gradient flows for the discrete Wasserstein distance. working paper or preprint, March 2016. [ bib | http | .pdf ]
Keywords: Gradient flows ; Wasserstein distance ; Finites Volumes discretization ; Fokker-Planck equation ; Heat equation ; Resistive Network ; Markov Kernel
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| [10] |
Qi-Rui Li, Filippo Santambrogio, and Xu-Jia Wang. Regularity in Monge’s mass transfer problem. Journal de Mathématiques Pures et Appliquées, pages In Press, Corrected Proof, only online for the moment, 2014. [ bib | http | .pdf ]
Keywords: monotone transport ; Ma-Trudinger-Wang ; Monge-Ampère equation
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| [11] |
Yann Brenier. A DOUBLE LARGE DEVIATION PRINCIPLE FOR MONGE-AMPERE GRAVITATION. working paper or preprint, March 2015. [ bib | http | .pdf ]
Keywords: Monge Ampere PDE ; optimal transport theory ; Gravitation modifiée ; large deviation theory
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| [12] |
Yann Brenier and xianglong duan. An integrable example of gradient flows based on optimal transport of differential forms. working paper or preprint, March 2017. [ bib | http | .pdf ]
Keywords: Optimal transport ; Differential forms ; Gradient Flow ; Relative entropy methods ; Dissipative solutions
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| [13] |
Yves Achdou and Mathieu Laurière. Mean field type control with congestion. working paper or preprint, April 2015. [ bib | http | .pdf ]
Keywords: congestion ; mean field type control ; weak solutions
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| [14] |
Bruno Bouchard, Xiaolu Tan, and Yiyi Zou. Numerical approximation of BSDEs using local polynomial drivers and branching processes. working paper or preprint, December 2016. [ bib | http | .pdf ]
Keywords: BSDE ; Numerical methods ; Branching process
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| [15] |
Adam Prosinski and Filippo Santambrogio. Global-in-time regularity via duality for congestion-penalized Mean Field Games. working paper or preprint, March 2016. [ bib | http | .pdf ]
Keywords: mean field games ; convex duality ; Wasserstein space ; Benamou-Brenier
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| [16] |
Guido De Philippis, Alpár Richard Mészáros, Filippo Santambrogio, and Bozhidar Velichkov. BV Estimates in Optimal Transportation and Applications. Archive for Rational Mechanics and Analysis, 219(2):829-860, February 2016. [ bib | DOI | http | .pdf ] |
| [17] |
Jean-David Benamou, Guillaume Carlier, and Luca Nenna. A Numerical Method to solve Optimal Transport Problems with Coulomb Cost. working paper or preprint, May 2015. [ bib | http | .pdf ] |
| [18] |
Bertrand Maury and Anthony Preux. Pressureless Euler equations with maximal density constraint : a time-splitting scheme. working paper or preprint, October 2015. [ bib | http | .pdf ]
Keywords: Pressureless Euler equations ; congestion ; optimal transportation
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| [19] |
Thomas Gallouët and Leonard Monsaingeon. A JKO SPLITTING SCHEME FOR KANTOROVICH-FISHER-RAO GRADIENT FLOWS. working paper or preprint, February 2016. [ bib | http | .pdf ]
Keywords: Unbalanced Optimal transport ; Wasserstein-Fisher-Rao ; Hellinger-Kantorovich ; Gradient flows ; JKO scheme
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| [20] |
Samer Dweik and Filippo Santambrogio. SUMMABILITY ESTIMATES ON TRANSPORT DENSITIES WITH DIRICHLET REGIONS ON THE BOUNDARY VIA SYMMETRIZATION TECHNIQUES. working paper or preprint, June 2016. [ bib | http | .pdf ]
Keywords: optimal transport ; Monge-Kantorovich equation ; minimal flows
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| [21] |
B Maury. Congested transport at microscopic and macroscopic scales. In 7th European Congress of Mathematics (7ECM), 7ECM Proceedings, Berlin, France, July 2016. [ bib | http | .pdf ]
Keywords: Continuity equation ; crowd motion ; optimal transportation ; Wasserstein space ; granular flows ; non-smooth analysis
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| [22] |
Martial Agueh and Guillaume Carlier. Generalized solutions of a kinetic granular media equation by a gradient flow approach. working paper or preprint, June 2015. [ bib | http | .pdf ]
Keywords: Kinetic models of granular media ; product Wasserstein space ; 35F25 ; 35D30 ; gradient flows AMS Subject Classifications: 35Q70
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| [23] |
Jean-David Benamou, Guillaume Carlier, and Nicolas Bonne. An Augmented Lagrangian Numerical approach to solving Mean-Fields Games. Research report, December 2013. [ bib | http | .pdf ]
Keywords: Mean field games ; Augmented Lagrangian ; Douglas Rachford
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| [24] |
Simone Di Marino, B Maury, and Filippo Santambrogio. Measure sweeping processes. working paper or preprint, December 2015. [ bib | http | .pdf ]
Keywords: Rotor Router Model ; Wasserstein distance ; Optimal transportation ; Sweeping process ; Subdifferential ; Differential inclusion
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| [25] |
Bruno Bouchard, Dylan Possamaï, Xiaolu Tan, and Chao Zhou. A unified approach to a priori estimates for supersolutions of BSDEs in general filtrations. Annales de l’Institut Henri Poincaré, September 2016. [ bib | http | .pdf ]
Keywords: reflected backward SDE ; Backward SDE ; supersolution ; Doob-Meyer decomposition
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| [26] |
Hugo Lavenant and Filippo Santambrogio. Optimal density evolution with congestion: L infinity bounds via flow interchange techniques and applications to variational Mean Field Games. working paper or preprint, May 2017. [ bib | http | .pdf ] |
| [27] |
Yves Achdou and Alessio Porretta. Convergence of a finite difference scheme to weak solutions of the system of partial differential equation arising in mean field games. working paper or preprint, March 2015. [ bib | http | .pdf ]
Keywords: finite difference schemes ; 9108 ; 91A23 ; 49L25 ; Mean field games ; 65M012 ; convergence AMS subject classifications 65M06
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| [28] |
Yves Achdou and Alessio Porretta. MEAN FIELD GAMES WITH CONGESTION. working paper or preprint, June 2017. [ bib | http | .pdf ] |
| [29] |
Yves Achdou, Martino Bardi, and Marco Cirant. MEAN FIELD GAMES MODELS OF SEGREGATION. working paper or preprint, December 2016. [ bib | http | .pdf ]
Keywords: segregation ; finite difference methods ; Mean Field Games ; multi-populations models ; large populations limit ; sys- ; systems of parabolic equations ; 49N70 ; 35K55
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| [30] |
Sylvain Faure and Bertrand Maury. Crowd motion from the granular standpoint. Mathematical Models and Methods in Applied Sciences, 2015. [ bib | DOI | http | .pdf ] |
| [31] |
Roman Andreev. Wavelet-in-time multigrid-in-space preconditioning of parabolic evolution equations. SIAM Journal on Scientific Computing, January 2016. [ bib | DOI | http | .pdf ]
Keywords: discretization ; parabolic ; space-time ; preconditioning ; wavelet ; multigrid
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| [32] |
Bruno Bouchard, Dylan Possamaï, and Xiaolu Tan. A general Doob-Meyer-Mertens decomposition for g-supermartingale systems. Electronic Journal of Probability, 21(36), 2016. [ bib | http | .pdf ]
Keywords: Backward stochastic differential equations MSC Classification (2010): 60H99 ; Doob-Meyer decomposition ; Non-linear expectations
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| [33] |
Thomas O Gallouët and Quentin Mérigot. A Lagrangian scheme for the incompressible Euler equation using optimal transport. working paper or preprint, June 2016. [ bib | http | .pdf ] |
| [34] |
Jean-David Benamou, Guillaume Carlier, and Maxime Laborde. An augmented Lagrangian approach to Wasserstein gradient flows and applications. working paper or preprint, December 2015. [ bib | http | .pdf ]
Keywords: Benamou-Brenier formulation ; augmented Lagrangian ; non-linear diffusion ; granular media ; systems ; crowd motions ; Wasserstein gradi-ent flows ; semi-implicit JKO scheme MS Classification 2010: 49M29 ; 65M60
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| [35] |
Jean-David Benamou and Guillaume Carlier. Augmented Lagrangian methods for transport optimization, Mean-Field Games and degenerate PDEs. working paper or preprint, October 2014. [ bib | http | .pdf ]
Keywords: Augmented Lagrangian ; Optimal Transport ; Monge Problem ; Mean-Field Games ; degenerate elliptic PDEs
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| [36] |
Martial Agueh and Guillaume Carlier. Vers un théorème de la limite centrale dans l’espace de Wasserstein ? working paper or preprint, December 2016. [ bib | http | .pdf ] |
| [37] |
Guillaume Carlier and Xavier Dupuis. An iterated projection approach to variational problems under generalized convexity constraints. working paper or preprint, December 2015. [ bib | http | .pdf ]
Keywords: Principal-agent problem ; b-convexity constraint ; convexity constraint ; convex envelopes ; iterated projections ; Dykstra’s algorithm Mathematics subject classification: 49M25 ; 65K15 ; 90C25
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| [38] |
Jean-David Benamou, Guillaume Carlier, and Filippo Santambrogio. Variational Mean Field Games. working paper or preprint, March 2016. [ bib | http | .pdf ] |
| [39] |
Bertrand Maury. Grains de foules, 2017. Texte à destination de mathématiciens non spécialistes du sujet, sur la prise en compte de la congestion dans les modèles microscopiques et macroscopiques de mouvements de foules. [ bib | http | .pdf ]
Keywords: Mouvements de foules ; inclusions différentielles ; processus de raffle ; transport optimal ; sphères dures
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| [40] |
Roman Andreev and Kristin Kirchner. Numerical methods for the 2nd moment of stochastic ODEs. working paper or preprint, November 2016. [ bib | http | .pdf ]
Keywords: Petrov-Galerkin discretizations ; Stochastic ordinary differential equations ; additive noise ; multiplicative noise ; variational problems ; Hilbert tensor product ; projective and injective tensor product
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| [41] |
Roman Andreev. Preconditioning the augmented Lagrangian method for instationary mean field games with diffusion. working paper or preprint, May 2017. [ bib | http | .pdf ]
Keywords: multigrid ; b-splines ; preconditioning ; space-time ; discretization ; mean field games ; augmented Lagrangian ; ALG2 ; ADMM
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| [42] |
Roman Andreev. Algorithm based fault tolerance with wavelets. working paper or preprint, September 2016. [ bib | http | .pdf ]
Keywords: algorithm based ; fault tolerance ; wavelets ; partial differential equations ; parallel computation
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| [43] |
Guillaume Carlier, Adam Oberman, and Edouard Oudet. Numerical methods for matching for teams and Wasserstein barycenters. ESAIM: Mathematical Modelling and Numerical Analysis, 49(6):1621-1642, November 2015. [ bib | DOI | http | .pdf ] |
| [44] |
Jean-David Benamou, Guillaume Carlier, Marco Cuturi, Luca Nenna, and Gabriel Peyré. Iterative Bregman Projections for Regularized Transportation Problems. SIAM Journal on Scientific Computing, 2(37):A1111-A1138, 2015. [ bib | DOI | http | .pdf ]
Keywords: Wasserstein barycenters ; entropy ; Optimal transport ; Bregman projection ; Kulback-Leibler divergence
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| [45] |
Clément Cancès, Thomas Gallouët, and Leonard Monsaingeon. Incompressible immiscible multiphase flows in porous media: a variational approach. working paper or preprint, 2016. [ bib | http | .pdf ]
Keywords: minimizing movement scheme ; constrained par-abolic system ; Multiphase porous media flows ; Wasserstein gradient flows
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| [46] |
Vincent Calvez and Thomas O. Gallouët. Blow-up phenomena for gradient flows of discrete homogeneous functionals. working paper or preprint, 2016. [ bib | http | .pdf ]
Keywords: discrete homogeneous functionals ; dichotomy theorem ; degenerate Keller-Segel equations ; drift diffusion equations ; Blow up
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| [47] |
Yves Achdou, Salomé Oudet, and Nicoletta Tchou. Asymptotic behavior of Hamilton-Jacobi equations defined on two domains separated by an oscillatory interface. working paper or preprint, July 2015. [ bib | http | .pdf ] |
| [48] |
Yves Achdou, Pierre-Noel Giraud, Jean-Michel Lasry, and Pierre-Louis Lions. A Long-Term Mathematical Model for Mining Industries. Applied Mathematics and Optimization, December 2016. [ bib | DOI | http | .pdf ]
Keywords: Heterogeneous agents model ; Mean field games ; Master equation ; Hamilton Jacobi equations ; Viscosity solution ; Model calibration
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| [49] |
Mathieu Fabre, Sylvain Faure, Mathieu Laurière, Bertrand Maury, and Charlotte Perrin. NON CLASSICAL SOLUTION OF A CONSERVATION LAW ARISING IN VEHICULAR TRAFFIC MODELLING *. ESAIM: Proceedings, 2016. [ bib | http | .pdf ]
Keywords: Traffic Flow Modeling ; Entropic Solutions ; Nonclassical Shocks
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