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Optimal Transportation and Applications

Efficient preconditioners for solving dynamical optimal transport via interior point methods

speaker: Enrico Facca (INRIA Lille Nord)

abstract: In this talk we address the numerical solution of the quadratic optimal transport problem in its dynamical form, the so-called Benamou-Brenier formulation. When solved using interior point methods, the main computational bottleneck is the solution via iterative methods of large saddle point linear systems arising from the associated Newton-Raphson scheme. We will present a preconditioner based on the partial commutation of the operators in the dual Schur complement of these linear systems. A series of numerical tests show that this preconditioner is the most efficient among those considered, with a CPU-time scaling only slightly more than linearly with respect to the number of unknowns used to discretize the problem.

timetable:
Tue 25 Oct, 11:45 - 12:10, Aula Magna Bruno Pontecorvo
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