Introduction to Optimal Transport
Introduktion till optimal transport

FRT305F, 4 credits

Valid from: Autumn 2023
Decided by: Maria Sandsten
Date of establishment: 2023-09-12

General Information

Division: Automatic Control
Course type: Third-cycle course
Teaching language: English

Aim

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.

Goals

Knowledge and Understanding

For a passing grade the doctoral student must

• - 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.

Competences and Skills

For a passing grade the doctoral student must be able to solve optimal transport problems using numerical methods.

Course Contents

- 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.

Course Literature

• 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.

Instruction Details

Type of instruction: Lectures

Examination Details

Examination format: Written report
Grading scale: Failed, pass
Examiner:

Admission Details

Admission requirements: Probability

Course Occasion Information

Contact and Other Information

Course coordinators:

• Pontus Giselsson <pontus.giselsson@control.lth.se>
• Dongjun Wu <dongjun.wu@control.lth.se>