# Fast iterative solvers for an optimal transport problem

@article{Herzog2019FastIS, title={Fast iterative solvers for an optimal transport problem}, author={Roland Herzog and John W. Pearson and M. Stoll}, journal={Advances in Computational Mathematics}, year={2019}, volume={45}, pages={495-517} }

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…

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