abstract: Optimal transport (OT) has become a fundamental mathematical tool at the interface between calculus of variations, partial differential equations and probability. It took however much more time for this notion to become mainstream in numerical applications. This situation is in large part due to the high computational cost of the underlying optimization problems. There is a recent wave of activity on the use of OT-related methods in fields as diverse as computer vision, computer graphics, statistical inference, machine learning and image processing.
In this short course, I will review numerical approaches for the approximate resolution of optimization problems related to optimal transport. I will also give some insight on how to apply these methods to imaging sciences and machine learning problems. The course will feature a numerical session using Python. Material for the course (including a small book, slides and computational resources) can be found online at https://optimaltransport.github.io/.