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math.OC2026
Semi-discrete convex order and Laguerre tessellation fitting
David P. Bourne, Thomas Gallouët, Quentin Mérigot +1
Laguerre tessellations offer an efficient way to parameterize a large class of convex partitions of Euclidean space using only a set of points and scalar weights. For this reason,…
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
Regularity theory and geometry of unbalanced optimal transport
Thomas Gallouët, Roberta Ghezzi, François-Xavier Vialard
Using the dual formulation only, we show that the regularity of unbalanced optimal transport also called entropy-transport inherits from the regularity of standard optimal transpor…