2022/06/05 by Said Kerrache, Kerrache, Said, Yasushi Nakauchi +1 · 1 citation
Engineering · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #FOS: Mathematics #Fluid Dynamics Simulations and Interactions #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Spacecraft Dynamics and Control
paper · pdf · doi:10.48550/arxiv.2206.13352
openalex publication_date 2022/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Optimal mass transport, also known as the earth mover's problem, is an optimization problem with important applications in various disciplines, including economics, probability theory, fluid dynamics, cosmology and geophysics to cite a few. Optimal transport has also found successful applications in image registration, content-based image retrieval, and more generally in pattern recognition and machine learning as a way to measure dissimilarity among data. This paper introduces the problem of constrained optimal transport. The time-dependent formulation, more precisely, the fluid dynamics approach is used as a starting point from which the constrained problem is defined by imposing a soft constraint on the density and momentum fields or restricting them to a subset of curves that satisfy some prescribed conditions. A family of algorithms is introduced to solve a class of constrained saddle point problems, which has convexly constrained optimal transport on closed convex subsets of the Euclidean space as a special case. Convergence proofs and numerical results are presented.