English

Vid tillräcklig efterfrågan

Optimal transport is a ubiquitous tool in various applications, such as image processing, machine learning and natural science. The course aims at giving a quick introduction to the fundamental theories of optimal transport, to help the students be able to do use optimal transport in their research work.

- fundamental theories of optimal transport, e.g., Kantorovich and Monge problems, structure of minimizers, Wasserstein spaces, geodesic structures, etc.,
- efficient numerical methods for computing optimal transport, e.g. Brenier-Benamou formula (continuous OT) and entropy regularization (discrete OT),
- some applications, e.g., Beckman's problem, image processing.

- know the various forms of optimal transport, e.g., Kantorovich, Monge, dual formulation, dynamic formulation,
- know the structures of the minimizers, e.g., c-cyclical monotonicity, convexity, etc.
- know some of the essential proofs in optimal transport.

be able to solve optimal transport problems using numerical methods.

Föreläsningar

Skriftlig rapport

Underkänd, godkänd

Probability

Ambrosio, L., Brué, E. & Semola, D.: Lectures on optimal transport. Springer, 2021.
Santambrogio, F.: Optimal transport for applied mathematicians. Springer, 2015.
Villani, C.: Topics in optimal transportation. American Mathematical Society, 2003.
Peyré, G. & Cuturi, M.: Computational optimal transport: With applications to data science. Foundations and Trends® in Machine Learning, 2019.

FRT305F

2023-09-12

Maria Sandsten