ANR project MAGA
The MAGA project is funded by the French ANR for four years (2016—2020). The acronym MAGA stands for Monge-Ampère et Géométrie Algorithmique.
Description
The Monge-Ampère equation is a fully nonlinear elliptic equation, which plays a central role in geometry and in the theory of optimal transport. However, the singular and non-linear nature of the equation is a serious obstruction to its efficient numerical resolution. The first aim of the MAGA project is to study and to implement discretizations of optimal transport and Monge-Ampère equations which rely on tools from computational geometry (Laguerre diagrams). In a second step, these solvers will be applied to concrete problems from various fields involving optimal transport or Monge-Ampère equations such as
- computational physics: early universe reconstruction problem, design of Lagrangian schemes handling congestion/incompressibility constraints
- economics: principal agent problems, urban planning, optimal pits design
- geometry: variational problems over convex bodies, reflector and refractor design for non-imaging optics
Laguerre diagram corresponding to the optimal transport between uniform measures over the unit ball and the so-called "tangle cube".
Fluid simulations using semi-discrete optimal transport.
Members
- Université Paris-Sud / Polytechnique
- Yann Brenier, École Polytechnique/CNRS
- Bertrand Maury, Université Paris-Sud
- Quentin Mérigot, Université Paris-Sud (coordinator)
- Luca Nenna, Université Paris-Sud
- Jean-Marie Mirebeau, Université Paris-Sud/CNRS
- Filippo Santambrogio, Université Lyon 1
- Université Paris-Dauphine / CNRS délégation régionale Paris B / Inria Paris
- Jean-David Benamou, Inria Paris
- Thomas Gallouet, Inria Paris
- Guillaume Carlier, Université Paris-Dauphine (local coordinator)
- François-Xavier Vialard, Université Paris-Est
- Université Grenoble-Alpes / Grenoble INP / Inria Nancy
- Dominique Attali, Grenoble-INP/CNRS
- Bruno Lévy, Inria Nancy
- Jocelyn Meyron, Grenoble-INP/Université Grenoble-Alpes
- Édouard Oudet, Université Grenoble-Alpes
- Boris Thibert, Université Grenoble-Alpes (local coordinator)