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math.OC2026
Polynomial diagrams for microstructure modelling
David P. Bourne, Maciej Buze, Thomas Gallouët +1
We formulate a framework of polynomial diagrams, which are a generalisation of power diagrams (PDs) and anisotropic power diagrams (APDs) allowing for boundaries between cells to b…
math.OC2024★ 1 cited
Constrained Hellinger-Kantorovich barycenters: least-cost soft and conic multi-marginal formulations
Maciej Buze
We show that the problem of finding the barycenter in the Hellinger-Kantorovich setting admits a least-cost soft multi-marginal formulation, provided that a one-sided hard marginal…
math.OC2023
Entropic regularisation of unbalanced optimal transportation problems
Maciej Buze, Manh Hong Duong
We develop a mathematical theory of entropic regularisation of unbalanced optimal transport problems. Focusing on static formulation and relying on the formalism developed for the…