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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.
|Number of pages||23|
|Journal||Advances in Computational Mathematics|
|Early online date||7 Aug 2018|
|Publication status||E-pub ahead of print - 7 Aug 2018|
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- 1 Finished
Fast Solvers for Real-World PDE-Constrained Optimization
1/08/17 → 31/05/18