2026/2027

Современная алгоритмическая оптимизация

Статус: Маго-лего

Кто читает: Департамент больших данных и информационного поиска

Где читается: Факультет компьютерных наук

Охват аудитории: для своего кампуса

Преподаватели: Гладин Егор Леонидович, Двинских Дарина Михайловна

Язык: русский

Кредиты: 3

Контактные часы: 28

Программа дисциплины

Аннотация

In this course we present the most important research directions in the modern Optimization Theory. The main topics of our interest are related to the provable complexity of optimization problems and the most efficient methods for finding their approximate solution. The main attention will be given to the methods for solving problems of large and super-large dimension, which arise in many engineering applications, telecommunications, and models for analyzing the Internet activity. We consider also the optimization schemes, which are necessary for justifying rationality of consumers in economic models. The most of the material is absent in the monographic literature. Therefore, we include in the course all necessary proofs.

Цель освоения дисциплины

• Provide provable complexity of optimization problems and the most efficient methods for finding their approximate solution.

Планируемые результаты обучения

• Know definition of optimization complexity
• Know universal first-order method. Be able to apply in practical problems

Содержание учебной дисциплины

• Complexity of optimization problems
• Universal first-order methods
• Second-order methods. Systems of nonlinear equations.
• Looking into the Black Box: Interior-point methods
• Looking into the Black Box: Smoothing technique
• Solving the huge-scale optimization problems.
• Algorithmic models of human behavior.
• Optimization with relative accuracy.

Элементы контроля

• Homeworks
• Project
• Exam

Промежуточная аттестация

• 2026/2027 2nd module
  0.3 * Homeworks + 0.4 * Exam + 0.3 * Project

Список литературы

Рекомендуемая основная литература

• Arkadi Nemirovski. (2001). Lectures on modern convex optimization. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.5E080C05

Рекомендуемая дополнительная литература

• Lu, H., Freund, R. M., & Nesterov, Y. (2018). Relatively Smooth Convex Optimization by First-Order Methods, and Applications. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.570D90A7

Авторы

• Двинских Дарина Михайловна