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Fast iterative solvers for an optimal transport problem

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https://link.springer.com/article/10.1007%2Fs10444-018-9625-5
Original languageEnglish
Number of pages23
JournalAdvances in Computational Mathematics
Early online date7 Aug 2018
DOIs
Publication statusE-pub ahead of print - 7 Aug 2018

Abstract

Optimal transport problems pose many challenges when considering their numerical treatment. We investigate the solution of a PDE-constrained optimisation problem subject to a particular transport equation arising from the modelling of image metamorphosis. We present the nonlinear optimisation problem, and discuss the discretisation and treatment of the nonlinearity via a Gauss-Newton scheme. We then derive preconditioners that can be used to solve the linear systems at the heart of the (Gauss-)Newton method.

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