2024/2025
Вариационное исчисление и оптимальное управление
Статус:
Дисциплина общефакультетского пула
Кто читает:
Факультет математики
Где читается:
Факультет математики
Когда читается:
1, 2 модуль
Охват аудитории:
для всех кампусов НИУ ВШЭ
Преподаватели:
Локуциевский Лев Вячеславович
Язык:
английский
Кредиты:
6
Course Syllabus
Abstract
The lectures provide an introduction to Calculus of Variations, addressing both classical subjects (action functionals, isoperimetric problems), and modern approaches (direct methods, applications to physics and optimal control). The student will be required to understand the theoretical aspects of the theory, as well as to apply it to specific cases.
Learning Objectives
- Understanding the modeling and interpretation of classical and modern variational problems. Knowledge of the basic techniques to identify optimal solutions to variational models.
Expected Learning Outcomes
- Being able to model various classes of a variational and optimal control problems, and derive sufficient and necessary conditions for extremality.
Course Contents
- Historical model problems and preliminaries: convex analysis, Sobolev spaces.
- Classical methods: Euler-Lagrange equations, optimal control, the Hamiltonian approach, viscosity solutions, applications.
- Direct methods: basic theory, elliptic problems (existence, uniqueness, regularity), Euler–Lagrange revisited, relaxation of integral functionals, applications.
Bibliography
Recommended Core Bibliography
- A first course in optimization theory, Sundaram, R. K., 2011
- Hogg, R. V., McKean, J. W., & Craig, A. T. (2014). Introduction to Mathematical Statistics: Pearson New International Edition. Harlow: Pearson. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1418145
Recommended Additional Bibliography
- Larsen, R. J., & Marx, M. L. (2015). An introduction to mathematical statistics and its applications. Slovenia, Europe: Prentice Hall. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.19D77756