Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation
CoRR(2023)
摘要
We present a discretization of the dynamic optimal transport problem for
which we can obtain the convergence rate for the value of the transport cost to
its continuous value when the temporal and spatial stepsize vanish. This
convergence result does not require any regularity assumption on the measures,
though experiments suggest that the rate is not sharp. Via an analysis of the
duality gap we also obtain the convergence rates for the gradient of the
optimal potentials and the velocity field under mild regularity assumptions. To
obtain such rates we discretize the dual formulation of the dynamic optimal
transport problem and use the mature literature related to the error due to
discretizing the Hamilton-Jacobi equation.
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