Infopaket

Mathematical programming

ВК 1.1

Вибіркова дисципліна для ОП

Second

2023/2024

3 Semester

5

Mastering the basic algorithms and methods of mathematical programming and gaining skills in their application to solve applied problems.

Full-time form

The student must have basic knowledge of higher mathematics and practical skills in programming.

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.

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.

Lectures, practical training, self-dependent work of students

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).

Ukrainian