Bachelor
2023/2024

# Methods of Optimization

Type:
Elective course (International Bachelor's in Business and Economics)

Area of studies:
Economics

Delivered by:
Department of Economics

When:
2 year, 1 module

Mode of studies:
offline

Open to:
students of one campus

Language:
English

ECTS credits:
4

Contact hours:
42

### 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

- Chapter 1. Introduction. Necessary mathematical apparatus. Extreme value theorem. Unconstrained optimization.
- Chapter 2. Some linear algebra material. Formulating general linear programming problems. Linear programming problems and graphic method of solving.
- Chapter 3. Lagrange multiplier. Sensitivity analysis.
- Chapter 4. Formulating non-linear programming problems.
- Chapter 5. The Karush–Kuhn–Tucker theorem.
- Chapter 6. Convex sets. Convex and concave functions. Convex optimization and Karush-Kuhn–Tucker conditions.
- Section 7. Solving optimization problems.

#### Assessment Elements

- Test 1Every problem has a number of points that are awarded for the correct solution. The points are written next to every problem in the test. If the points are not indicated, then every problem weighs the same number of points. Total points for every test equal to 10. Note: correct answers assume correct solutions to be presented. If there is no solution to the problem or it is incorrect, the points may not be awarded even if the answer is correct.
- Test 2Every problem has a number of points that are awarded for the correct solution. The points are written next to every problem in the test. If the points are not indicated, then every problem weighs the same number of points. Total points for every test equal to 10. Note: correct answers assume correct solutions to be presented. If there is no solution to the problem or it is incorrect, the points may not be awarded even if the answer is correct
- Test 3Every problem has a number of points that are awarded for the correct solution. The points are written next to every problem in the test. If the points are not indicated, then every problem weighs the same number of points. Total points for every test equal to 10. Note: correct answers assume correct solutions to be presented. If there is no solution to the problem or it is incorrect, the points may not be awarded even if the answer is correct.
- Test 4
- Test 5Every problem has a number of points that are awarded for the correct solution. The points are written next to every problem in the test. If the points are not indicated, then every problem weighs the same number of points. Total points for every test equal to 10. Note: correct answers assume correct solutions to be presented. If there is no solution to the problem or it is incorrect, the points may not be awarded even if the answer is correct.
- Test 6
- ActivityThe teacher evaluates students’ seminar work: their activity during a seminar, successful solving of the given problems, their preparation for the seminars (including homework). The cumulative grade on a 10-point scale for the seminar work is calculated before the final control and goes into Oaud.
- Final testing (exam)