An Efficient Numerical Approximation for the Monge-Kantorovich Mass Transfer Problem

Avendaño-Garrido, Martha Lorena; Gabriel-Arguelles, J. Rigoberto; Quintana-Torres, Ligia; Mezura-Montes, Efrén

doi:10.1007/978-3-319-27926-8_20

Cited by 1 publication

(2 citation statements)

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“…Thus, as a heuristic technique to improve the solution, we check the values c 6 , µ σ 6 associated with each solution µ σ Using the solution µ * 5 which is given by Figure 10, the information of the high-pass components (Figures 7, 8 and 9) and Lemma 1, we obtain a feasible solution for Level 6, which is denoted by μ6 . Finally, we present Table 1 that compare the solutions of the MK problem, in which MK 5 is the value associated with the optimal solution µ * 5 at level of discretization j − 1 = 5, MK 6 is the value associated with an optimal solution µ * 6 at level of discretization j = 6, and MK σ * 6 is the value associated with the solution µ σ * 6 obtained by the heuristic method described in the previous paragraph. For the points of Type II, we apply a permutation to the solution over the two points that improve the solution and repeat the process with the rest of the points.…”

Section: Methodological Proposalmentioning

confidence: 99%

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Efficient Method to Solve the Monge–Kantarovich Problem Using Wavelet Analysis

Acosta-Portilla,

González-Flores,

López-Martínez

et al. 2023

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In this paper, we present and justify a methodology to solve the Monge–Kantorovich mass transfer problem through Haar multiresolution analysis and wavelet transform with the advantage of requiring a reduced number of operations to carry out. The methodology has the following steps. We apply wavelet analysis on a discretization of the cost function level j and obtain four components comprising one corresponding to a low-pass filter plus three from a high-pass filter. We obtain the solution corresponding to the low-pass component in level j−1 denoted by μj−1*, and using the information of the high-pass filter components, we get a solution in level j denoted by μ^j. Finally, we make a local refinement of μ^j and obtain the final solution μjσ.

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Section: Methodological Proposalmentioning

confidence: 99%

“…Moreover, they gave an error bound for the numerical approximation. A generalization of this scheme of approximation was presented in [4,5]. They proposed an approximation scheme for the Monge-Kantorovich (MK) mass transfer problem on compact spaces that consisted of reducing to solve a sequence of finite transport problems.…”

Section: Introductionmentioning

confidence: 99%