# Guillaume Carlier

#40,886

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French mathematician

## Guillaume Carlier's AcademicInfluence.com Rankings

Guillaume Carliermathematics Degrees

Mathematics

#5025

World Rank

#7097

Historical Rank

Game Theory

#31

World Rank

#35

Historical Rank

Measure Theory

#3145

World Rank

#3730

Historical Rank

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Mathematics

## Why Is Guillaume Carlier Influential?

(Suggest an Edit or Addition)According to Wikipedia, Guillaume Carlier is a French mathematician. Most of his work lies in the field of calculus of variation and optimization. He is a professor of applied mathematics at Paris Dauphine University and a researcher at Mokaplan, a joint INRIA-CNRS-Université Paris-Dauphine team dedicated to research in the field of optimal transport.

## Guillaume Carlier's Published Works

### Published Works

- Barycenters in the Wasserstein Space (2011) (679)
- Iterative Bregman Projections for Regularized Transportation Problems (2014) (649)
- Convergence of Entropic Schemes for Optimal Transport and Gradient Flows (2015) (148)
- Deep relaxation: partial differential equations for optimizing deep neural networks (2017) (127)
- Matching for teams (2010) (126)
- Augmented Lagrangian Methods for Transport Optimization, Mean Field Games and Degenerate Elliptic Equations (2015) (117)
- NUMERICAL METHODS FOR MATCHING FOR TEAMS AND WASSERSTEIN BARYCENTERS (2014) (106)
- Optimal Transportation with Traffic Congestion and Wardrop Equilibria (2006) (106)
- A general existence result for the principal-agent problem with adverse selection (2001) (102)
- Core of convex distortions of a probability (2003) (99)
- Variational Mean Field Games (2017) (97)
- From Knothe's Transport to Brenier's Map and a Continuation Method for Optimal Transport (2008) (85)
- Vector quantile regression: An optimal transport approach (2014) (82)
- OPTIMAL DEMAND FOR CONTINGENT CLAIMS WHEN AGENTS HAVE LAW INVARIANT UTILITIES (2010) (81)
- Congested traffic dynamics, weak flows and very degenerate elliptic equations (2010) (78)
- On a Class of Multidimensional Optimal Transportation Problems (2003) (77)
- Discretization of functionals involving the Monge–Ampère operator (2014) (74)
- Duality and existence for a class of mass transportation problems and economic applications (2003) (69)
- Pareto efficiency for the concave order and multivariate comonotonicity (2009) (64)
- An augmented Lagrangian approach to Wasserstein gradient flows and applications (2016) (63)
- Rearrangement inequalities in non-convex insurance models (2005) (63)
- Two-persons efficient risk-sharing and equilibria for concave law-invariant utilities (2008) (61)
- Pareto efficient insurance contracts when the insurer's cost function is discontinuous (2003) (58)
- OPTIMAL TRANSPORTATION FOR THE DETERMINANT (2006) (52)
- Optimal Transport and Cournot-Nash Equilibria (2012) (52)
- On a weighted total variation minimization problem (2007) (51)
- Geodesics for a class of distances in the space of probability measures (2012) (51)
- Generalized incompressible flows, multi-marginal transport and Sinkhorn algorithm (2017) (45)
- Equilibrium structure of a bidimensional asymmetric city (2007) (40)
- The Structure of Cities (2004) (40)
- A numerical approach to variational problems subject to convexity constraint (2001) (39)
- Law invariant concave utility functions and optimization problems with monotonicity and comonotonicity constraints (2006) (39)
- Regularity of solutions for some variational problems subject to a convexity constraint (2001) (38)
- On the selection of maximal Cheeger sets (2007) (38)
- A Numerical Method to Solve Multi-Marginal Optimal Transport Problems with Coulomb Cost (2016) (37)
- From Nash to Cournot–Nash equilibria via the Monge–Kantorovich problem (2014) (37)
- APPROXIMATION OF MAXIMAL CHEEGER SETS BY PROJECTION (2009) (36)
- A variational model for urban planning with traffic congestion (2005) (36)
- Tomographic Reconstruction from a Few Views: A Multi-Marginal Optimal Transport Approach (2017) (35)
- Derivatives with respect to metrics and applications: subgradient marching algorithm (2010) (35)
- Existence and monotonicity of solutions to moral hazard problems (2005) (34)
- On certain anisotropic elliptic equations arising in congested optimal transport: Local gradient bounds (2014) (34)
- 3. Distributed and boundary control problems for the semidiscrete Cahn–Hilliard/Navier–Stokes system with nonsmooth Ginzburg–Landau energies (2017) (32)
- An entropy minimization approach to second-order variational mean-field games (2018) (30)
- On some optimal control problems governed by a state equation with memory (2008) (29)
- Numerical approximation of continuous traffic congestion equilibria (2009) (28)
- Efficient Insurance Contracts under Epsilon-Contaminated Utilities (2003) (28)
- A continuous theory of traffic congestion and Wardrop equilibria (2012) (24)
- Optimal derivatives design for mean–variance agents under adverse selection (2007) (21)
- A Differential Approach to the Multi-Marginal Schrödinger System (2018) (20)
- A costly state verification model with diversity of opinions (2005) (20)
- Vector Quantile Regression (2014) (20)
- A numerical solution to Monge’s problem with a Finsler distance as cost (2018) (20)
- A splitting method for nonlinear diffusions with nonlocal, nonpotential drifts (2016) (19)
- Pareto optima and equilibria when preferences are incompletely known (2013) (18)
- Optimal Transportation and Economic Applications (2010) (17)
- Exponential convergence for a convexifying equation (2012) (17)
- Calculus of variations with convexity constraint (2002) (17)
- From discrete to continuous Wardrop equilibria (2012) (17)
- A strategy for non-strictly convex transport costs and the example of $¦x-y¦^p$ in $R2$ (2009) (16)
- Remarks on existence and uniqueness of Cournot–Nash equilibria in the non-potential case (2014) (16)
- Debt contracts with ex-ante and ex-post asymmetric information: an example (2006) (16)
- Convex Bodies of Optimal Shape (1997) (15)
- Vector quantile regression beyond the specified case (2017) (14)
- Congested Traffic Equilibria and Degenerate Anisotropic PDEs (2013) (13)
- Augmented Lagrangian methods for transport optimization, Mean-Field Games and degenerate PDEs (2014) (12)
- Core of convex distortions of a probability on a non atomic space (2001) (12)
- A monotonic algorithm for the optimal control of the Fokker-Planck equation (2008) (12)
- Entropic-Wasserstein Barycenters: PDE Characterization, Regularity, and CLT (2020) (11)
- H1-projection into the set of convex functions : a saddle-point formulation (2001) (11)
- Vector quantile regression and optimal transport, from theory to numerics (2020) (10)
- Remarks on continuity equations with nonlinear diffusion and nonlocal drifts (2016) (10)
- Convergence rate of general entropic optimal transport costs (2022) (10)
- On the Linear Convergence of the Multimarginal Sinkhorn Algorithm (2022) (10)
- Optimal spatial pricing strategies with transportation costs (2013) (10)
- Partial differential equations for training deep neural networks (2017) (10)
- Insurance Contracts with deductibles and upper limits (2002) (9)
- Optimal monopoly pricing with congestion and random utility via partial mass transport (2018) (9)
- On the total variation Wasserstein gradient flow and the TV-JKO scheme (2017) (9)
- Approximation of variational problems with a convexity constraint by PDEs of Abreu type (2019) (9)
- A Numerical Method to solve Optimal Transport Problems with Coulomb Cost (2015) (9)
- Hamilton-Jacobi-Bellman equations for the optimal control of a state equation with memory (2009) (9)
- Optimal transportation and the structure of cities (2003) (9)
- Topological Optimization and Optimal Transport: In the Applied Sciences (2017) (9)
- A PROJECTION APPROACH TO THE NUMERICAL ANALYSIS OF LIMIT LOAD PROBLEMS (2011) (8)
- Existence and monotonicity of optimal debt contracts in costly state verification models (2003) (8)
- A numerical approach for a class of risk-sharing problems (2011) (8)
- A Γ-Convergence Result for the Upper Bound Limit Analysis of Plates (2014) (8)
- Computation of Cournot–Nash Equilibria by Entropic Regularization (2016) (8)
- Vector quantile regression beyond correct specification (2016) (8)
- On systems of continuity equations with nonlinear diffusion and nonlocal drifts (2015) (8)
- Differentiability properties of rank-linear utilities (2008) (7)
- On the Wasserstein distance between mutually singular measures (2018) (7)
- SISTA: Learning Optimal Transport Costs Under Sparsity Constraints (2020) (6)
- Representation of the polar cone of convex functions and applications (2008) (6)
- 4. High-order topological expansions for Helmholtz problems in 2D (2017) (5)
- Variational Methods for Tomographic Reconstruction with Few Views (2018) (5)
- Are generalized call-spreads efficient ? (2007) (5)
- A Planning Problem Combining Calculus of Variations and Optimal Transport (2011) (5)
- On the minimizing movement with the 1-Wasserstein distance (2018) (4)
- Optimal regions for congested transport (2014) (4)
- On Monge's Problem for Bregman-like Cost Functions (2007) (4)
- An Iterated Projection Approach to Variational Problems Under Generalized Convexity Constraints (2017) (4)
- A system of inequalities arising in mathematical economics and connected with the Monge-Kantorovich problem (2002) (3)
- On Pontryagin's Principle for the Optimal Control of some State Equations with Memory (2010) (3)
- Representation of the core of convex measure games via Kantorovich potentials (2005) (3)
- Convex geometry of finite exchangeable laws and de Finetti style representation with universal correlated corrections (2021) (3)
- Exponential convergence for a convexifying equation and a non-autonomous gradient flow for global minimization (2010) (3)
- Generalized solutions of a kinetic granular media equation by a gradient flow approach (2015) (3)
- Quantitative Stability of Barycenters in the Wasserstein Space (2022) (3)
- Nonparametric Adverse Selection Problems (2002) (3)
- REMARKS ON A CLASS OF KINETIC MODELS OF GRANULAR MEDIA: ASYMPTOTICS AND ENTROPY BOUNDS (2015) (3)
- Lipschitz Continuity of the Schr\"odinger Map in Entropic Optimal Transport (2022) (3)
- 8. Weak Monge–Ampère solutions of the semi-discrete optimal transportation problem (2017) (3)
- RETRACTED: Congested traffic dynamics, weak flows and very degenerate elliptic equations (2010) (2)
- A mean field game model for the evolution of cities (2021) (2)
- A planning problem combining optimal control and optimal transport (2009) (2)
- Equilibrium in quality markets, beyond the transferable case (2019) (2)
- Optimal Transport meets Probability, Statistics and Machine Learning (2017) (2)
- A note on wage differentials, fixed-wages and adverse selection (2002) (2)
- An Augmented Lagrangian Numerical approach to solving Mean-Fields Games (2013) (2)
- TESTING ADVERSE SELECTION AND MORAL HAZARD ON FRENCH CAR INSURANCE DATA (2013) (1)
- Correction to: Vector quantile regression and optimal transport, from theory to numerics (2020) (1)
- A class of total variation minimization problems on the whole space (2009) (1)
- Labor Contracts With Two-Dimensional Adverse Selection (2000) (1)
- Optimal debt contracts and diversity of opinions: an extreme case of bunching (2003) (1)
- On Dynkin's model of economic equilibrium under uncertainty (2001) (1)
- Fixed-Wages, Wage Differentials and Worker Heterogeneities (2008) (1)
- A Necessary and SuÆcient Optimality Condition for a Class of Nonconvex Scalar Variational Problems (2004) (1)
- Classical and Modern Optimization (2021) (1)
- Computing the demand of agents with a law invariant utility (2006) (1)
- Existence of solutions to principal-agent problems under general preferences and non-compact allocation space (2019) (1)
- 5. On a new phase field model for the approximation of interfacial energies of multiphase systems (2017) (0)
- Softening Bilevel Problems Via Two-scale Gibbs Measures (2019) (0)
- Vector quantile regression and optimal transport, from theory to numerics (2020) (0)
- Existence of solutions to principal–agent problems with adverse selection under minimal assumptions (2019) (0)
- Thomas Lachand-Robert--memorial volume. (2008) (0)
- ESAIM: Control, Optimisation and Calculus of Variations (2005) (0)
- Computation of Cournot–Nash Equilibria by Entropic Regularization (2017) (0)
- On Some Systems Controlled by the Structure of Their Memory (2010) (0)
- Ju n 20 12 OPTIMAL TRANSPORT AND COURNOT-NASH EQUILIBRIA (2012) (0)
- Visible . A Service of zbw (2014) (0)
- A Spatial Pareto Exchange Economy Problem (2023) (0)
- Correction to: Vector quantile regression and optimal transport, from theory to numerics (2020) (0)
- SISTA : Learning Optimal Transport Costs under Sparsity Constraints (2022) (0)
- Entropic approximation of $\infty$-optimal transport problems (2023) (0)
- Generalized incompressible flows, multi-marginal transport and Sinkhorn algorithm (2018) (0)
- Wasserstein interpolation with constraints and application to a parking problem (2022) (0)
- Programme on “ Optimal Transport ” April 15 – June 14 , 2019 organized (2019) (0)
- Restrictions and identification in a multidimensional risk-sharing problem (2014) (0)
- A simple city equilibrium model with an application to teleworking (2022) (0)
- A mean field model for the interactions between firms on the markets of their inputs (2022) (0)
- COMONOTONIC MEASURES OF MULTIVARIATE RISKS IVAR EKELAND University of British Columbia ALFRED GALICHON (2010) (0)
- Fixed-wages, wages differentials : the role of workers'heterogeinities (2003) (0)
- Equilibrium in quality markets, beyond the transferable case (2018) (0)

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## What Schools Are Affiliated With Guillaume Carlier?

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