Aug 27, 2013
Tuesday

11:00 AM  12:00 PM


Prescribeddivergence problems in optimal transportation
Filippo Santambrogio (Université de Paris XI)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
 The classical Monge problem (but only with cost $xy$, and not $xy^2$) has an equivalent counterpart which is the minimization of the $L^1$ norm of a vector field $v$, subject to the constraint $\nabla\cdot v=\mu\nu$. This is a minimal flow problem introduced by M. Beckmann in the '50s without knowing the relation with the works by Kantorovich. It has recently come back into fashion because of its possible variants, where the cost rather than being linear as in the $L^1$ norm can be made convex (thus taking into account for congestion effects) or concave (favoring joint transportation). Also, wellposedness of this problem and regularity issues about the optimal $v$ have brought many questions about the socalled transport density, a measure of the local amount of traffic during the transportation which is naturally associated to these 1homogeneous transport problems.
I will present the problem using in particular some recent approach based on the flow by DacorognaMoser, and give the main results on the transport density
 Supplements

v1135
536 KB application/pdf



Aug 28, 2013
Wednesday

09:00 AM  10:00 AM


Prescribeddivergence problems in optimal transportation
Filippo Santambrogio (Université de Paris XI)

 Location
 MSRI:
 Video

 Abstract
 The classical Monge problem (but only with cost $xy$, and not $xy^2$) has an equivalent counterpart which is the minimization of the $L^1$ norm of a vector field $v$, subject to the constraint $\nabla\cdot v=\mu\nu$. This is a minimal flow problem introduced by M. Beckmann in the '50s without knowing the relation with the works by Kantorovich. It has recently come back into fashion because of its possible variants, where the cost rather than being linear as in the $L^1$ norm can be made convex (thus taking into account for congestion effects) or concave (favoring joint transportation). Also, wellposedness of this problem and regularity issues about the optimal $v$ have brought many questions about the socalled transport density, a measure of the local amount of traffic during the transportation which is naturally associated to these 1homogeneous transport problems.
I will present the problem using in particular some recent approach based on the flow by DacorognaMoser, and give the main results on the transport density
 Supplements

v1138
520 KB application/pdf



Aug 30, 2013
Friday

09:30 AM  10:30 AM


Prescribeddivergence problems in optimal transportation
Filippo Santambrogio (Université de Paris XI)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
 The classical Monge problem (but only with cost $xy$, and not $xy^2$) has an equivalent counterpart which is the minimization of the $L^1$ norm of a vector field $v$, subject to the constraint $\nabla\cdot v=\mu\nu$. This is a minimal flow problem introduced by M. Beckmann in the '50s without knowing the relation with the works by Kantorovich. It has recently come back into fashion because of its possible variants, where the cost rather than being linear as in the $L^1$ norm can be made convex (thus taking into account for congestion effects) or concave (favoring joint transportation). Also, wellposedness of this problem and regularity issues about the optimal $v$ have brought many questions about the socalled transport density, a measure of the local amount of traffic during the transportation which is naturally associated to these 1homogeneous transport problems.
I will present the problem using in particular some recent approach based on the flow by DacorognaMoser, and give the main results on the transport density
 Supplements

v1146
522 KB application/pdf


