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Regular version of the site
Master 2020/2021

Modern Algorithmical Optimization

Type: Compulsory course (Statistical Learning Theory)
Area of studies: Applied Mathematics and Informatics
Delivered by: Department of Complex System Modelling Technologies
When: 2 year, 1, 2 module
Mode of studies: distance learning
Master’s programme: Statistical Learning Theory
Language: English
ECTS credits: 6

Course Syllabus

Abstract

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.
Learning Objectives

Learning Objectives

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

Expected Learning Outcomes

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

Course Contents

  • 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.
Assessment Elements

Assessment Elements

  • non-blocking Экзамен
    Оценка за дисциплину выставляется в соответствии с формулой оценивания от всех пройденных элементов контроля. Экзамен не проводится.
  • non-blocking Homework
Interim Assessment

Interim Assessment

  • Interim assessment (2 module)
    0.5 * Homework + 0.5 * Экзамен
Bibliography

Bibliography

Recommended Core Bibliography

  • 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

Recommended Additional Bibliography

  • 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