Fast iterative solvers for an optimal transport problem

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Roland Herzog, John W. Pearson, Martin Stoll

Published: 2019, Last Modified: 07 May 2024Adv. Comput. Math. 2019EveryoneRevisionsBibTeXCC BY-SA 4.0
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.