Methods of Optimization

2026/2027

Academic Year

ENG

Instruction in English

3

ECTS credits

Delivered at:

Department of Economics

Course type:

Compulsory course

When:

2 year, 1 module

Instructors

Свиридов Олег Игоревич

Telekhov, Ignaty I.

Course Syllabus

Abstract

The objectives of mastering the discipline "Methods of optimal solutions" is to study the relevant sections of methods for solving optimization problems, allowing the student to navigate the course "Mathematical models in Economics". The course "Methods of optimal solutions" will be used in the theory and applications of multidimensional mathematical analysis, mathematical economics, econometrics.

Learning Objectives

• The goal of mastering «Methods of Optimization I» is to study corresponding chapters of methods of solving optimization problems that would allow for students to navigate through the «Mathematical models in economics» course. «Methods of Optimization I» will be used in theoretic and applied parts of mathematical analysis, microeconomics, game theory, econometrics. Course materials might come in handy in developing and application of numerical methods for solving wide range of problems throughout different fields of knowledge, building and researching mathematical models in economics. This discipline is a model application instrument for economics students to study as a mathematical component of their specialized education.

Expected Learning Outcomes

• demonstrates knowledge of actions with matrices and the ability to set a linear programming problem and solve it graphically
• demonstrates knowledge of the Kuhn-Tucker theorem with proofs
• demonstrates knowledge of the Lagrange function and economic interpretation of coefficients
• demonstrates the ability to calculate the derivative and differential, determines the global and local maximum and minimum
• knows the properties of convex and concave functions, Slater's condition

Course Contents

• 1. Introduction. The necessary mathematical apparatus. The Weierstrass theorem. The task of unconditional optimization
• 2. Some information from linear algebra. General statement of the linear programming problem. A linear programming problem and a graphical solution method
• 3. Lagrange method and Kuhn-Tucker theorem
• 4. Sufficient conditions for a global maximum
• 5. Multi-criteria optimization
• 6. The envelope theorem
• 7. Combinatorial optimization

Assessment Elements

• Test № 1
• Test № 6
• Test № 4
• Final exam
• Test № 2
• Test № 3
• Seminar work
• Test № 5

Interim Assessment

• 2026/2027 1st module
  0.11 * Test № 1 + 0.11 * Test № 6 + 0.09 * Seminar work + 0.11 * Test № 2 + 0.25 * Final exam + 0.11 * Test № 4 + 0.11 * Test № 3 + 0.11 * Test № 5

Bibliography

Recommended Core Bibliography

• Красс, М. С.  Математика в экономике: математические методы и модели : учебник для среднего профессионального образования / М. С. Красс, Б. П. Чупрынов ; под редакцией М. С. Красса. — 2-е изд., испр. и доп. — Москва : Издательство Юрайт, 2021. — 541 с. — (Профессиональное образование). — ISBN 978-5-9916-9136-9. — Текст : электронный // Образовательная платформа Юрайт [сайт]. — URL: https://urait.ru/bcode/477849 (дата обращения: 04.07.2025).

Recommended Additional Bibliography

• Методы оптимальных решений : Учеб. пособие, Ногин, В.Д., 2006
• Сборник задач по исследованию операций : учеб. пособие для вузов, Аронович, А. Б., 1997