The purpose of this workshop is to bring together a diverse group of mathematicians and other scientists to discuss dynamical and numerical aspects of optimal transport. Optimal transport provides a natural geometry for characterizing and studying many evolutionary partial differential equations. In particular, their dynamics is seen to possess either a gradient flow or Hamiltonian structure when viewed on a manifold endowed with an optimal transport metric. These connections have found diverse applications, ranging from fluid mechanics to materials microstructure evolution and Ricci flow.
Algorithms for numerical transport optimization have applications in a variety of areas such as image processing, medicine, computational cosmology, geosciences, or urban transport. Numerical transport optimization methods have not yet reached their full capacity where they can meet the most demanding practical applications. For example, in cosmology, effective handling of galaxy catalogues with millions of entries for reconstruction of early velocities according to the Zeldovich model is a big challenge. Up to now, there are two principal numerical approaches to optimal transport: In one approach, one chooses a suitable numerical discretization, and optimal transport becomes a large scale combinatorial optimization problem. Alternatively, transport plans can be generated by solutions to suitable partial differential equations. Both cases and their comparison with recent second order cone programming (SOCP) methods that are particularly popular in image processing will be discussed.
Yann Brenier
(Université de Nice Sophia Antipolis)
Karl Glasner
(University of Arizona)
Allen Tannenbaum
(Georgia Institute of Technology)
Richard Tsai
(University of Texas at Austin)
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