160 citations · 237 across the 8 of their papers we have counts for
8 papers
Local matching indicators for transport with concave costs
Julie Delon, Julien Salomon, A. Sobolevskii
In this note, we introduce a class of indicators that enable to compute efficiently optimal transport plans associated to arbitrary distributions of demands and supplies in…
The Monge-Ampère-Kantorovich approach to reconstruction in cosmology
Roya Mohayaee, Andrei Sobolevskii
Motion of a continuous fluid can be decomposed into an "incompressible" rearrangement, which preserves the volume of each infinitesimal fluid element, and a gradient map that trans…
Reconstruction of the early Universe as a convex optimization problem
Y. Brenier, U. Frisch, M. Henon +4
We show that the deterministic past history of the Universe can be uniquely reconstructed from the knowledge of the present mass density field, the latter being inferred from the 3…
Reconstruction of the primordial Universe by a Monge--Ampere--Kantorovich optimisation scheme
R. Mohayaee, U. Frisch, S. Matarrese +1
A method for the reconstruction of the primordial density fluctuation field is presented. Various previous approaches to this problem rendered {\it non-unique} solutions. Here, it…
Exact interval solutions to the discrete Bellman equation and polynomial complexity of problems in interval idempotent linear algebra
Grigori Litvinov, Andrei Sobolevskii
In this note we construct a solution of a matrix interval linear equation of the form X=AX+B (the discrete stationary Bellman equation) over partially ordered semirings, including…
Idempotent mathematics and interval analysis
Grigori Litvinov, Viktor Maslov, Andrei Sobolevskii
A brief introduction into Idempotent Mathematics and an idempotent version of Interval Analysis are presented. Some applications are discussed.