Fast iterative solvers for an optimal transport problem - Herzog, Roland; Pearson, John W.; Stoll, Martin (Advances in computational mathematics, 2019)
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.