Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

An Entropic Optimal Transport Numerical Approach to the Reflector Problem

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, as discussed in particular in [Ramdas et al., 2017] [Genevay et al., 2018] [Feydy et al., 2018], is another important tool to achieve reasonable results. The paper reviews the necessary mathematical and numerical tools needed to produce and discuss the obtained numerical results. We find that Sinkhorn algorithm may be adapted, at least in simple academic cases, to the resolution of the far field reflector problem. Sinkhorn canonical extension to continuous potentials is needed to generate continuous reflector approximations. The use of Sinkhorn divergences [Feydy et al., 2018] is useful to mitigate the entropic bias.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [14 references]  Display  Hide  Download
Contributor : Jean-David Benamou <>
Submitted on : Friday, April 10, 2020 - 1:18:26 PM
Last modification on : Wednesday, September 23, 2020 - 4:30:26 AM


Files produced by the author(s)


  • HAL Id : hal-02539799, version 1



Jean-David Benamou, Wilbert Ijzerman, Giorgi Rukhaia. An Entropic Optimal Transport Numerical Approach to the Reflector Problem. 2020. ⟨hal-02539799⟩



Record views


Files downloads