Магистратура
2025/2026
Оптимальный транспорт и его приложения
Лучший по критерию «Полезность курса для Вашей будущей карьеры»
Лучший по критерию «Полезность курса для расширения кругозора и разностороннего развития»
Лучший по критерию «Новизна полученных знаний»
Статус:
Курс по выбору (Математика машинного обучения)
Где читается:
Факультет компьютерных наук
Охват аудитории:
для своего кампуса
Язык:
английский
Кредиты:
3
Контактные часы:
40
Course Syllabus
Abstract
This course introduces students to the fundamental concepts of optimal transport theory and its wide range of applications in various fields such as economics, machine learning, image processing, and statistics. Through a combination of theoretical lectures and practical exercises, participants will gain both conceptual understanding and hands-on experience with this powerful mathematical framework.
Learning Objectives
- The course aims at presenting the basic results in the field of Optimal Transport
Expected Learning Outcomes
- Known about the Monge and Kantorovich formulations of the Optimal Transport problem
- Understand general conditions under which an optimal transport plan exists
- Be familiar with Kantorovich-Wasserstein distances and their main properties
- Know about conditions under which an optimal transport map exists and learn about their particular structure (Brenier Theorem)
- Understand the connection between the OT problem and a particular partial differential equation known as the Continuity Equation
- Know about the formal Riemannian structure that can be put on the 2-Kantorovich-Wasserstein space
Course Contents
- The Optimal Transport Problem
- Existence of optimal Transport plans
- Kantorovich-Wasserstein distances
- Necessary and sufficient optimality conditions
- Existence of optimal transport maps
- Duality
- Continuity equation
- The formal Riemannian structure of W2
Bibliography
Recommended Core Bibliography
- Villani, C. (2009). Optimal Transport : Old and New. Berlin: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=261958
Recommended Additional Bibliography
- Gabriel Peyré, & Marco Cuturi. (2019). Computational Optimal Transport : With Applications to Data Science. Norwell, MA: Now Publishers. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=2241984