Julie Delon
Local matching indicators for transport problems with concave costs.
Thu, 02/10/2011 - 16:01 — SomNambulAuthors: Julie Delon, Julien Salomon, Andrei Sobolevskii
Subjects: Optimization and Control
AbstractIn this paper, we introduce a class of indicators that enable to compute
efficiently optimal transport plans associated to arbitrary distributions of N
demands and M supplies in R in the case where the cost function is concave. The
computational cost of these indicators is small and independent of N. A
hierarchical use of them enables to obtain an efficient algorithm.Local matching indicators for concave transport costs.
Wed, 12/02/2009 - 16:01 — SomNambulAuthors: Julie Delon, Julien Salomon, A. Sobolevskii
Subjects: Optimization and Control
AbstractIn this note, we introduce a class of indicators that enable to compute
efficiently optimal transport plans associated to arbitrary distributions of
$N$ demands and $N$ supplies in $\mathbf{R}$ in the case where the cost
function is concave. The cost of these indicators is small and independent of
$N$. Using them recursively according to a particular algorithm allows to find
an optimal transport plan in less than $N^2$ evaluations of the cost function.Fast transport optimization for Monge costs on the circle.
Fri, 10/09/2009 - 18:27 — SomNambulAuthors: Julie Delon, Julien Salomon, Andrei Sobolevskii
Subjects: Optimization and Control
AbstractConsider the problem of optimally matching two measures on the circle, or
equivalently two periodic measures on the real line, and suppose the cost of
matching two points satisfies the Monge condition. We introduce a notion of
locally optimal transport plan, motivated by the weak KAM (Aubry-Mather)
theory, and show that all locally optimal transport plans are conjugate to
shifts and that the cost of a locally optimal transport plan is a convex
function of a shift parameter.
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