Minimizing Flows for the Monge–Kantorovich Problem
Tannenbaum, Allen R.
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In this work, we formulate a new minimizing flow for the optimal mass transport (Monge–Kantorovich) problem. We study certain properties of the flow, including weak solutions as well as short- and long-term existence. Optimal transport has found a number of applications, including econometrics, fluid dynamics, cosmology, image processing, automatic control, transportation, statistical physics, shape optimization, expert systems, and meteorology.