Mathematical programming

Course: Computer Systems and Networks

Structural unit: Faculty of Radiophysics, Electronics and Computer Systems

Title
Mathematical programming
Code
ВК 1.1
Module type
Вибіркова дисципліна для ОП
Educational cycle
Second
Year of study when the component is delivered
2021/2022
Semester/trimester when the component is delivered
4 Semester
Number of ECTS credits allocated
5
Learning outcomes
Mastering the basic algorithms and methods of mathematical programming and gaining skills in their application to solve applied problems.
Form of study
Full-time form
Prerequisites and co-requisites
The student must have basic knowledge of higher mathematics and practical skills in programming.
Course content
General mathematical model of linear programming problem. Classification of linear programming problems. Graphical method for solving the problem of linear programming. Simplex method of solving the problem of linear programming. Duality theory in linear programming. Transport problem and method of potentials for its solution. Homorrie methods, branches and boundaries, decay vectors for solving the problem of integer linear programming. Statement, geometric interpretation and some algorithms for solving the problem of parametric linear programming. Gradient methods for solving unconditional optimization problems: gradient method with step crushing, the fastest gradient descent method and their geometric interpretation. Apply the fastest descent method to solving systems of linear algebraic equations. Methods of one-dimensional minimization of unimodal and multiextreme functions.
Recommended or required reading and other learning resources/tools
1. Іксанов О.М., Шевченко В.І. Транспортна задача, її властивості та методи розв’язування — Київ: Наукове видавництво "ТВіМС", 2010. — 84 с. http://csc.knu.ua/uk/library/books/iksanov-26.pdf 2. Попов Ю.Д., Тюптя В.І., Шевченко В.І. Методи оптимізації — Київ: Електронне видання. Електронна бібліотека факультету кібернетики Київського національного університету імені Тараса Шевченка, 2003, — 215 с. http://csc.knu.ua/uk/library/books/popov-30.pdf 3. Тюптя В.І., Шевченко В.І., Стрюк В.К. Динамічне та нелінійне програмування — Київ: Електронне видання. Електронна бібліотека факультету кібернетики Київського національного університету імені Тараса Шевченка, 2003. — 30 с. http://csc.knu.ua/uk/library/books/tiuptia-31.pdf. 4. Brian D. Bunday. Basic Linear Programming Paperback — E. Arnold, 1984. – 163 p. 5. Dimitri P. Bertsekas. Dynamic Programming and Optimal Control. — Athena Scientific, 2012. — 1270 p.
Planned learning activities and teaching methods
Lectures, practical training, self-dependent work of students
Assessment methods and criteria
The grade for studying the course consists of grades for current test tasks (up to 40 points), modular tests (up to 20 points) and grades for final control test (up to 40 points).
Language of instruction
Ukrainian

Lecturers

This discipline is taught by the following teachers

Tetiana Mykhailivna Proshchenko
Department of mathematics and Theoretical Radio Physics
Faculty of Radiophysics, Electronics and Computer Systems

Departments

The following departments are involved in teaching the above discipline

Department of mathematics and Theoretical Radio Physics
Faculty of Radiophysics, Electronics and Computer Systems