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Multiresolution analysis applied to the Monge-Kantorovich problem. (English) Zbl 1470.49070

Summary: We give a scheme of approximation of the MK problem based on the symmetries of the underlying spaces. We take a Haar type MRA constructed according to the geometry of our spaces. Thus, applying the Haar type MRA based on symmetries to the MK problem, we obtain a sequence of transportation problem that approximates the original MK problem for each of MRA. Moreover, the optimal solutions of each level solution converge in the weak sense to the optimal solution of original problem.

MSC:

49Q20 Variational problems in a geometric measure-theoretic setting
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
65T60 Numerical methods for wavelets
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