publication . Other literature type . Article . Preprint . 2020

An Entropic Optimal Transport Numerical Approach to the Reflector Problem

Benamou, Jean-David; Ijzerman, Wilbert L.; Rukhaia, Giorgi;
Open Access English
  • Published: 17 Apr 2020
  • Publisher: Zenodo
  • Country: France
Abstract
The point source far field reflector design problem is one of the main classic optimal transport problems with a non-euclidean displacement cost [Wang, 2004] [Glimm and Oliker, 2003].This work describes the use of Entropic Optimal Transport and the associated Sinkhorn algorithm [Cuturi, 2013] to solve it numerically. As the reflector modelling is based on the Kantorovich potentials, several questions arise. First, on the convergence of the discrete entropic approximation and here we follow the recent work of [Berman, 2017] and in particular the imposed discretization requirements therein. Secondly, the correction of the Entropic bias induced by the Entropic OT, ...
Subjects
free text keywords: [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Funded by
EC| ROMSOC
Project
ROMSOC
Reduced Order Modelling, Simulation and Optimization of Coupled systems
  • Funder: European Commission (EC)
  • Project Code: 765374
  • Funding stream: H2020 | MSCA-ITN-EID
Validated by funder
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Zenodo
Other literature type . 2020
Provider: Datacite
Zenodo
Other literature type . 2020
Provider: Datacite
Hal-Diderot
Preprint . 2020
Provider: Hal-Diderot
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