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French applied mathematician
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.
[1]
[2]
Carlier's work mainly focuses on applied mathematics, in particular in the fields of
calculus of variations,
optimization,
convex analysis, and
transportation theory as well as their application to
economics and traffic modelling.
[1]
[3]
[4]
He graduated in mathematics and mathematical economics from
ENSAE ParisTech,
Pierre and Marie Curie University, and Paris-Dauphine University in 1996. He then completed his PhD at Paris-Dauphine University in 2000, with a dissertation on the applications of calculus of variations to contract theory, under the supervision of
Ivar Ekeland.
[5] After his studies, he was an assistant professor at the
University of Bordeaux and then moved to Paris-Dauphine University, where he is now a professor.
[1] He is a member of Mokaplan,
[2] a joint research unit co-sponsored by Paris-Dauphine University, the
National Centre for Scientific Research, and the
French Institute for Research in Computer Science and Automation.
[6]
- Agueh, Martial; Carlier, Guillaume (2011).
"Barycenters in the Wasserstein Space". SIAM Journal on Mathematical Analysis. 43 (2). Society for Industrial and Applied Mathematics: 904–924.
doi:
10.1137/100805741.
S2CID
8592977.
- Benamou, Jean-David; Carlier, Guillaume (2015).
"Augmented Lagrangian Methods for Transport Optimization, Mean Field Games and Degenerate Elliptic Equations". Journal of Optimization Theory and Applications. 167. Springer: 1–26.
doi:
10.1007/s10957-015-0725-9.
S2CID
254741013.
- Benamou, Jean-David; Carlier, Guillaume; Cuturi, Marco; Nenna, Luca; Peyré, Gabriel (2015).
"Iterative Bregman Projections for Regularized Transportation Problems". SIAM Journal on Scientific Computing. 37 (2). Society for Industrial and Applied Mathematics: A1111–A1138.
arXiv:
1412.5154.
doi:
10.1137/141000439.
S2CID
12631372.
- Carlier, Guillaume (2001).
"A general existence result for the principal-agent problem with adverse selection". Journal of Mathematical Economics. 35. Elsevier: 129–150.
doi:
10.1016/S0304-4068(00)00057-4.
- Carlier, Guillaume; Ekeland, Ivar (2010).
"Matching for teams". Economic Theory. 42 (2). Springer: 397–418.
doi:
10.1007/s00199-008-0415-z.
S2CID
56567818.
- Carlier, Guillaume; Duval, Vincent; Peyré, Gabriel; Schmitzer, Bernhard (2017).
"Convergence of Entropic Schemes for Optimal Transport and Gradient Flows". SIAM Journal on Mathematical Analysis. 49 (2). Society for Industrial and Applied Mathematics: 1385–1418.
arXiv:
1512.02783.
doi:
10.1137/15M1050264.
S2CID
46156175.
- Carlier, Guillaume; Galichon, Alfred; Santambrogio, Filippo (2010).
"From Knothe's transport to Brenier's map and a continuation method for optimal transport". SIAM Journal on Mathematical Analysis. 41 (6). Society for Industrial and Applied Mathematics: 2554–2576.
arXiv:
0810.4153.
doi:
10.1137/080740647.
S2CID
15795393.
- Chaudhari, Pratik; Oberman, Adam; Osher, Stanley; Soatto, Stefano; Carlier, Stefano (2018).
"Deep relaxation: partial differential equations for optimizing deep neural networks". Research in the Mathematical Sciences. 5 (3). Springer.
arXiv:
1704.04932.
doi:
10.1007/s40687-018-0148-y.
S2CID
2074215.
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