CEREMADE
Carlier Guillaume
Full Professor
Publications
Articles
Carlier G., Dupuis X., Rochet J-C., Thanassoulis J. (2024), A General Solution to the Quasi Linear Screening Problem, Journal of Mathematical Economics, vol. 114 
Carlier G., Chizat L., Laborde M. (2024), Displacement smoothness of entropic optimal transport, Control, Optimisation and Calculus of Variations, vol. 30, p. 24
Carlier G., Pegon P., Tamanini L. (2023), Convergence rate of general entropic optimal transport costs, Calculus of Variations and Partial Differential Equations, vol. 62, n°4
Carlier G., Delalande A., Mérigot Q. (2023), Quantitative Stability of Barycenters in the Wasserstein Space, Probability Theory and Related Fields
Achdou Y., Carlier G., Petit Q., Tonon D. (2023), A mean field model for the interactions between firms on the markets of their inputs, Mathematical and Financial Economics
Carlier G. (2022), On the linear convergence of the multi-marginal Sinkhorn algorithm, SIAM Journal on Optimization, vol. 32, n°2
Carlier G., Friesecke G., Vögler D. (2022), Convex geometry of finite exchangeable laws and de Finetti style representation with universal correlated corrections, Probability Theory and Related Fields, p. 44
Carlier G., Chernozhukov V., De Bie G., Galichon A. (2022), Correction to: Vector quantile regression and optimal transport, from theory to numerics, Empirical Economics, vol. 62, n°1, p. 63-63
Carlier G., Eichinger K., Kroshnin A. (2021), Entropic-Wasserstein barycenters: PDE characterization, regularity and CLT, SIAM Journal on Mathematical Analysis, vol. 53, n°5, p. 5880–5914
Barilla C., Carlier G., Lasry J-M. (2021), A mean field game model for the evolution of cities, Journal of Dynamics and Games, vol. 8, n°3, p. 299-329
Carlier G., Zhang K. (2020), Existence of solutions to principal–agent problems with adverse selection under minimal assumptions, Journal of Mathematical Economics, vol. 88, p. 64 - 71
Carlier G., Laborde M. (2020), A differential approach to the multi-marginal Schrödinger system, SIAM Journal on Mathematical Analysis, vol. 52, n°1, p. 12
Carlier G., Poon C. (2019), On the total variation Wasserstein gradient flow and the TV-JKO scheme, ESAIM. Control, Optimisation and Calculus of Variations, vol. 25, p. 21
Benamou J-D., Carlier G., Nenna L. (2019), Generalized incompressible flows, multi-marginal transport and Sinkhorn algorithm, Numerische Mathematik, vol. 142, p. 33–54
Benamou J-D., Carlier G., Marino S., Nenna L. (2019), An entropy minimization approach to second-order variational mean-field games, Mathematical Models and Methods in Applied Sciences, vol. 29, n°8, p. 1553-1583
Carlier G., Radice T. (2019), Approximation of variational problems with a convexity constraint by PDEs of Abreu type, Calculus of Variations and Partial Differential Equations, vol. 58, p. 16
Carlier G., Mallozzi L. (2019), Softening bilevel problems via two-scale Gibbs measures, Set-Valued and Variational Analysis, vol. 30, p. 573–595
Blanchet A., Carlier G., Nenna L. (2018), Computation of Cournot-Nash equilibria by entropic regularization, Vietnam Journal of Mathematics, vol. 46, n°1, p. 15-31
Carlier G., Mallozzi L. (2018), Optimal monopoly pricing with congestion and random utility via partial mass transport, Journal of Mathematical Analysis and Applications, vol. 457, n°2, p. 1218-1231
Benamou J-D., Carlier G., Hatchi R. (2018), A numerical solution to Monge's problem with a Finsler distance as cost, ESAIM: Mathematical Modelling and Numerical Analysis, vol. 52, n°6 (November-December 2018 ), p. 2133 - 2148
Bergounioux M., Abraham I., Abraham R., Carlier G., Le Pennec E., Trélat E. (2018), Variational methods for tomographic reconstruction with few views, Milan Journal of Mathematics, vol. 86, n°2, p. 157--200
Buttazzo G., Carlier G., Laborde M. (2018), On the Wasserstein distance between mutually singular measures, Advances in Calculus of Variations, vol. 13, n°2, p. 141–154
Agueh M., Carlier G., Igbida N. (2018), On the minimizing movement with the 1-Wasserstein distance, ESAIM. Control, Optimisation and Calculus of Variations, vol. 24, n°4 (October–December 2018 ), p. 1415 - 1427
Abraham I., Abraham R., Bergounioux M., Carlier G. (2017), Tomographic reconstruction from a few views: a multi-marginal optimal transport approach, Applied Mathematics and Optimization, vol. 75, n°1, p. 55-73
Carlier G., Galichon A., Chernozhukov V. (2017), Vector quantile regression beyond the specified case, Journal of Multivariate Analysis, vol. 161, p. 96-102
Agueh M., Carlier G. (2017), Vers un théorème de la limite centrale dans l'espace de Wasserstein ?, Comptes rendus. Mathématique, vol. 355, n°7, p. 812-818
Carlier G., Duval V., Peyré G., Schmitzer B. (2017), Convergence of Entropic Schemes for Optimal Transport and Gradient Flows, SIAM Journal on Mathematical Analysis, vol. 49, n°2, p. 1385-1418
Carlier G., Dupuis X. (2017), An iterated projection approach to variational problems under generalized convexity constraints, Applied Mathematics and Optimization, vol. 76, n°3, p. 565-592
Carlier G., Chernozhukov V., Galichon A. (2016), Vector Quantile Regression: An optimal transport approach, Annals of Statistics, vol. 44, n°3, p. 1165-1192
Benamou J-D., Carlier G., Mérigot Q., Oudet E. (2016), Discretization of functionals involving the Monge-Ampère operator, Numerische Mathematik, vol. 134, n°3, p. 611-636
Bleyer J., Carlier G., Duval V., Mirebeau J-M., Peyré G. (2016), A Γ-Convergence Result for the Upper Bound Limit Analysis of Plates, ESAIM: Mathematical Modelling and Numerical Analysis, vol. 50, n°1, p. 215-235
Agueh M., Carlier G. (2016), Generalized solutions of a kinetic granular media equation by a gradient flow approach, Calculus of Variations and Partial Differential Equations, vol. 55, n°2
Blanchet A., Carlier G. (2016), Optimal transport and Cournot-Nash equilibria, Mathematics of Operations Research, vol. 41, n°3, p. 125-145
Benamou J-D., Carlier G., Laborde M. (2016), An augmented Lagrangian approach to Wasserstein gradient flows and applications, ESAIM: Proceedings and Surveys, vol. 54, p. 1-17
Carlier G., Laborde M. (2016), A splitting method for nonlinear diffusions with nonlocal, nonpotential drifts, Nonlinear Analysis, vol. 150, p. 1-18
Benamou J-D., Carlier G., Cuturi M., Nenna L., Peyré G. (2015), Iterative Bregman Projections for Regularized Transportation Problems, SIAM Journal on Scientific Computing, vol. 37, n°2, p. A1111–A1138
Carlier G., Oberman A., Oudet E. (2015), Numerical methods for matching for teams and Wasserstein barycenters, ESAIM: Mathematical Modelling and Numerical Analysis, vol. 49, n°6, p. 1621-1642
Agueh M., Carlier G., Illner R. (2015), Remarks on a class of kinetic models of granular media: asymptotics and entropy bounds, Kinetic & Related Models, vol. 8, n°2, p. 201-214
Benamou J-D., Carlier G. (2015), Augmented Lagrangian Methods for Transport Optimization, Mean Field Games and Degenerate Elliptic Equations, Journal of Optimization Theory and Applications, vol. 167, n°1, p. 1-26
Buttazzo G., Carlier G., Guarino lo Bianco S. (2015), Optimal regions for congested transport, ESAIM: Mathematical Modelling and Numerical Analysis, vol. 49, n°6, p. 1607-1619
Blanchet A., Carlier G. (2014), Remarks on existence and uniqueness of Cournot-Nash equilibria in the non-potential case, Mathematics and Financial Economics, vol. 8, n°4, p. 417-433
Carlier G., Blanchet A. (2014), From Nash to Cournot-Nash equilibria via the Monge-Kantorovich problem, Philosophical Transactions. Physical, Mathematical and Engineering Sciences, vol. 372, n°2028, p. n°20130398
Carlier G., Aloqeili M., Ekeland I. (2014), Restrictions and identification in a multidimensional risk-sharing problem, Economic Theory, vol. 56, n°2, p. 409-423
Brasco L., Carlier G. (2013), On certain anisotropic elliptic equations arising in congested optimal transport: local gradient bounds, Advances in Calculus of Variations, vol. 7, n°3, p. 379–407
Carlier G., Nazaret B., Cardaliaguet P. (2013), Geodesics for a class of distances in the space of probability measures, Calculus of Variations and Partial Differential Equations, vol. 48, n°3-4, p. 395-420
Brasco L., Carlier G. (2013), Congested traffic equilibria and degenerate anisotropic PDEs, Dynamic Games and Applications, vol. 3, n°4, p. 508-522
Dana R-A., Carlier G. (2013), Pareto optima and equilibria when preferences are incompletely known, Journal of Economic Theory, vol. 148, n°4, p. 1606-1623
Carlier G., Dacorogna B. (2012), Résolution du problème de Dirichlet pour lʼéquation du Jacobien prescrit via lʼéquation de Monge–Ampère, Comptes rendus. Mathématique, vol. 350, n°7-8, p. 371-374
Galichon A., Carlier G. (2012), Exponential convergence for a convexifying equation, ESAIM. Control, Optimisation and Calculus of Variations, vol. 18, n°3, p. 611-620
Carlier G., Baillon J-B. (2012), From discrete to continuous Wardrop equilibria, Networks and Heterogeneous Media, vol. 7, n°2, p. 219-241
Carlier G., Dana R-A., Galichon A. (2012), Pareto efficiency for the concave order and multivariate comonotonicity, Journal of Economic Theory, vol. 147, n°1, p. 207-229
Carlier G., Santambrogio F. (2012), A continuous theory of traffic congestion and Wardrop equilibria, Journal of Mathematical Sciences, vol. 181, n°6, p. 792-804
Lachapelle A., Carlier G. (2011), A numerical approach for a class of risk-sharing problems, Journal of Mathematical Economics, vol. 47, n°1, p. 1-13
Ionescu I., Comte M., Carlier G., Peyré G. (2011), A Projection Approach to the Numerical Analysis of Limit Load Problems, Mathematical Models and Methods in Applied Sciences, vol. 21, n°6, p. 1291-1316
Lachapelle A., Carlier G. (2011), A Planning Problem Combining Calculus of Variations and Optimal Transport, Applied Mathematics and Optimization, vol. 63, n°1, p. 1-9
Carlier G., Agueh M. (2011), Barycenters in the Wasserstein space, SIAM Journal on Mathematical Analysis, vol. 43, n°2, p. 904-924
Carlier G., Dana R-A. (2011), Optimal Demand for Contingent Claims when Agents have law Invariant Utilities, Mathematical Finance, vol. 21, n°2, p. 169-201
Santambrogio F., Carlier G., Galichon A. (2010), From Knothe's transport to Brenier's map and a continuation method for optimal transport, SIAM Journal on Mathematical Analysis, vol. 41, n°6, p. 2554-2576
Tahraoui R., Carlier G., Houmia A. (2010), On Pontryagin's Principle for the Optimal Control of some State Equations with Memory, Journal of Convex Analysis, vol. 17, n°3-4, p. 1007-1017
Carlier G., Ekeland I. (2010), Matching for Teams, Economic Theory, vol. 42, n°2, p. 397-418
Tahraoui R., Buttazzo G., Carlier G. (2010), On Some Systems Controlled by the Structure of Their Memory, SIAM Journal on Control and Optimization, vol. 48, n°8, p. 5241-5253
Carlier G., Santambrogio F., Peyré G., Benmansour F. (2010), Derivatives with respect to metrics and applications: Subgradient Marching Algorithm, Numerische Mathematik, vol. 116, n°3, p. 357-381
Carlier G., Brasco L., Santambrogio F. (2010), Congested traffic dynamics, weak flows and very degenerate elliptic equations, Journal de mathématiques pures et appliquées, vol. 93, n°6, p. 652-671
Carlier G., Santambrogio F., de Pascale L. (2010), A strategy for non-strictly convex transport costs and the example of ║x−y║p in R2, Communications in Mathematical Sciences, vol. 8, n°4, p. 931-941
Carlier G., Tahraoui R. (2010), Hamilton-Jacobi-Bellman equations for the optimal control of a state equation with memory, ESAIM. Control, Optimisation and Calculus of Variations, vol. 16, n°3, p. 744-763
Comte M., Peyré G., Carlier G. (2009), Approximation of Maximal Cheeger Sets by Projection, ESAIM: Mathematical Modelling and Numerical Analysis, vol. 43, n°1, p. 139-150
Agueh M., Carlier G. (2009), A class of total variation minimization problems on the whole space, Nonlinear Analysis, vol. 70, n°6, p. 2356-2365
Carlier G., Benmansour F., Santambrogio F., Peyré G. (2009), Numerical Approximation of Continuous Traffic Congestion Equilibria, Networks and Heterogeneous Media, vol. 4, n°3, p. 605-623
Carlier G. (2008), Differentiability properties of Rank-Linear Utilities, Journal of Mathematical Economics, vol. 44, n°1, p. 15-23
Carlier G., Nazaret B. (2008), Optimal transportation for the determinant, ESAIM. Control, Optimisation and Calculus of Variations, vol. 14, n°4, p. 678-698
Lachand-Robert T., Carlier G. (2008), Representation of the polar cone of convex functions and applications, Journal of Convex Analysis, vol. 15, n°3, p. 535-546
Dana R-A., Carlier G. (2008), Two-Persons Efficient Risk-Sharing and Equilibria for Concave Law-Invariant Utilities, Economic Theory, vol. 36, n°2, p. 189-223
Carlier G., Tahraoui R. (2008), On some optimal control problems governed by a state equation with memory, ESAIM. Control, Optimisation and Calculus of Variations, vol. 14, n°4, p. 725-743
Jimenez C., Santambrogio F., Carlier G. (2008), Optimal transportation with traffic congestion and Wardrop equilibria, SIAM Journal on Control and Optimization, vol. 47, n°3, p. 1330-1350
Gaumont D., Carlier G. (2008), Fixed-Wages, Wage Differentials and Workers Heterogeneities, Australian Economic Papers, vol. 47, n°4, p. 320-333
Carlier G., Comte M. (2008), Thomas Lachand-Robert--memorial volume., Journal of Convex Analysis, vol. 15, n°3, p. 455-458
Carlier G. (2008), Remarks on Toland's duality, convexity constraint and optimal transport, Pacific Journal of Optimization, vol. 4, n°3, p. 423-432
Ekeland I., Carlier G. (2007), Equilibrium structure of a bidimensional asymmetric city, Nonlinear Analysis: Real World Applications, vol. 8, n°3, p. 725-748
Carlier G., Dana R-A. (2007), Are generalized call-spreads efficient ?, Journal of Mathematical Economics, vol. 43, n°5, p. 581-596
Carlier G., Comte M. (2007), On a weighted total variation minimization problem, Journal of Functional Analysis, vol. 250, n°1, p. 214-226
Touzi N., Ekeland I., Carlier G. (2007), Optimal derivatives design for mean–variance agents under adverse selection, Mathematics and Financial Economics, vol. 1, n°1, p. 57-80
Comte M., Buttazzo G., Carlier G. (2007), On the selection of maximal Cheeger sets, Differential and Integral Equations, vol. 20, n°9, p. 991-1004
Jimenez C., Carlier G. (2007), On Monge's Problem for Bregman-like Cost Functions, Journal of Convex Analysis, vol. 14, n°3, p. 647-655
Renou L., Carlier G. (2006), Debt contracts with ex-ante and ex-post asymmetric information: an example, Economic Theory, vol. 28, n°2, p. 461-473
Dana R-A., Carlier G. (2006), Law invariant concave utility functions and optimization problems with monotonicity and comonotonicity constraints, Statistics & Decisions, vol. 24, n°1, p. 127-152
Carlier G., Dana R-A. (2005), Rearrangement inequalities in non-convex insurance models, Journal of Mathematical Economics, vol. 41, n°4-5, p. 483-503
Dana R-A., Carlier G. (2005), Existence and monotonicity of solutions to moral hazard problems, Journal of Mathematical Economics, vol. 41, n°7, p. 826-843
Carlier G., Ekeland I. (2004), The Structure of Cities, Journal of Global Optimization, vol. 29, n°4, p. 371-376
Carlier G., Dana R-A. (2003), Core of convex distortions of a probability, Journal of Economic Theory, vol. 113, n°2, p. 199-222
Shahidi N., Carlier G., Dana R-A. (2003), Efficient Insurance Contracts under Epsilon-Contaminated Utilities, The Geneva Papers on Risk and Insurance. Theory, vol. 28, n°1, p. 59-71
Dana R-A., Carlier G. (2003), Pareto efficient insurance contracts when the insurer's cost function is discontinuous, Economic Theory, vol. 21, n°4, p. 871-893
Carlier G. (2002), Nonparametric Adverse Selection Problems, Annals of Operations Research, vol. 114, n°1-4, p. 71-82
Carlier G., Gaumont D. (2002), A note on wage differentials, fixed-wages and adverse selection, Economics Letters, vol. 77, n°3, p. 349-356
Carlier G. (2002), Calculus of variations with convexity constraint, Journal of Nonlinear and Convex Analysis, vol. 3, n°2, p. 125-143
Evstigneev I., Carlier G. (2001), On Dynkin's model of economic equilibrium under uncertainty, Economics Bulletin, vol. 3, n°12, p. 1-8
Lachand-Robert T., Carlier G. (2001), Regularity of solutions for some variational problems subject to a convexity constraint, Communications on Pure and Applied Mathematics, vol. 54, n°5, p. 583-594
Lachand-Robert T., Carlier G., Maury B. (2001), H1-projection into the set of convex functions : a saddle-point formulation, ESAIM: Proceedings and Surveys, vol. 10, p. 277-289
Maury B., Carlier G., Lachand-Robert T. (2001), A numerical approach to variational problems subject to convexity constraint, Numerische Mathematik, vol. 88, n°2, p. 299-318
Chapitres d'ouvrage
Benamou J-D., Carlier G., Nenna L. (2017), A Numerical Method to Solve Multi-Marginal Optimal Transport Problems with Coulomb Cost, in Glowinski R., Osher S., Yin W., Splitting Methods in Communication, Imaging, Science, and Engineering Springer, p. 577-601
Benamou J-D., Carlier G., Santambrogio F. (2017), Variational Mean Field Games, in Nicola Bellomo, Pierre Degond, Eitan Tadmor, Active Particles, Volume 1, Paris: Springer, p. 141-171
Carlier G. (2003), Duality and existence for a class of mass transportation problems and economic applications, in Maruyama, T., Advances in Mathematical Economics, 5, Berlin: Springer, p. 200
Communications avec actes
Buttazzo G., Carlier G. (2010), Optimal spatial pricing strategies with transportation costs, in Zalavski, Alexander, Nonlinear Analysis and Optimization II: Optimization, Providence (R.I.), American Mathematical Society, 290 p.
Carlier G., Salomon J. (2008), A monotonic algorithm for the optimal control of the Fokker-Planck equation, in , 47th IEEE Conference on Decision and Control.CDC 2008. Proceedings, Cancun, IEEE - Institute of Electrical and Electronics Engineers, 269-273 p.
Prépublications / Cahiers de recherche
Carlier G., Figalli A., Santambrogio F. (2024), On optimal transport maps between 1/d-concave densities, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 17 p.
Carlier G., Malamut H. (2024), Well-posedness and convergence of entropic approximation of semi-geostrophic equations, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 21 p.
Carlier G., Chizat L., Laborde M. (2024), Displacement smoothness of entropic optimal transport, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 20 p.
Carlier G., Chenchene E., Eichinger K. (2023), Wasserstein medians: robustness, PDE characterization and numerics, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 38 p.
Carlier G., Delalande A., Mérigot Q. (2023), Quantitative Stability of the Pushforward Operation by an Optimal Transport Map, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 23 p.
Brizzi C., Carlier G., de Pascale L. (2023), Entropic approximation of $\infty$-optimal transport problems, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 30 p.
Carlier G., Benamou J-D., Matthes D. (2023), Wasserstein gradient flow of the Fisher information from a non-smooth convex minimization viewpoint, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 21 p.
Carlier G., Pegon P., Tamanini L. (2023), Convergence rate of general entropic optimal transport costs, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 31 p.
Carlier G. (2022), Fenchel-Young inequality with a remainder and applications to convex duality and optimal transport, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 10 p.
Achdou Y., Carlier G., Petit Q., Tonon D. (2022), A simple city equilibrium model with an application to teleworking, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 32 p.
Buttazzo G., Carlier G., Eichinger K. (2022), Wasserstein interpolation with constraints and application to a parking problem, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 30 p.
Achdou Y., Carlier G., Petit Q., Tonon D. (2022), A mean field model for the interactions between firms on the markets of their inputs, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 29 p.
Carlier G., Dupuy A., Galichon A., Sun Y. (2021), SISTA : learning optimal transport costs under sparsity constraints, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 21 p.
Bacon X., Carlier G., Nazaret B. (2021), A spatial Pareto exchange economy problem, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 30 p.
Carlier G., Laborde M. (2015), On systems of continuity equations with nonlinear diffusion and nonlocal drifts, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 26 p.
Ekeland I., Carlier G. (2003), Optimal transportation and the structure of cities, Paris, Université Paris-Dauphine, 34 p.
Carlier G., Levin V., Ekeland I., Shananin A. (2002), A system of inequalities arising in mathematical economics and connected with the Monge-Kantorovich problem, Paris, Cahiers du CEREMADE, 13 p.
Carlier G., Dana R-A. (2002), Insurance Contracts with deductibles and upper limits, Paris, Cahiers du CEREMADE, 21 p.
Evstigneev I., Carlier G. (2001), Dynkin's model of economic equilibrium under uncertainty, Cahiers du CEREMADE, 13 p.
Dana R-A., Carlier G. (2001), Core of convex distortions of a probability on a non atomic space, Cahiers du CEREMADE, 26 p.
Gaumont D., Carlier G. (2000), Labor Contracts With Two-Dimensional Adverse Selection, Paris, Cahiers du CEREMADE, 20 p.
Rapports
Benamou J-D., Bonne N., Carlier G. (2013), Une méthode numérique utilisant un Lagrangien augmenté pour la résolution de jeux à champs moyens, Il Mulino, 27 p.