Fast iterative solvers for an optimal transport problem

Roland Herzog; John Pearson; Martin Stoll

doi:10.1007/s10444-018-9625-5

Fast iterative solvers for an optimal transport problem

Roland Herzog, John Pearson, Martin Stoll

School of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Number of pages	23
Journal	Advances in Computational Mathematics
Early online date	7 Aug 2018
DOIs	https://doi.org/10.1007/s10444-018-9625-5
Publication status	E-pub ahead of print - 7 Aug 2018

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HPS18Accepted author manuscript, 558 KB

https://link.springer.com/article/10.1007%2Fs10444-018-9625-5

Fast Solvers for Real-World PDE-Constrained Optimization
Pearson, J.
EPSRC
1/08/17 → 31/05/18
Project: Research

Cite this

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Fast iterative solvers for an optimal transport problem

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Fast Solvers for Real-World PDE-Constrained Optimization

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