Optimization Methods

Major: Applied mathematics and computer science
Code of subject: 6.113.00.O.055
Credits: 5.00
Department: Applied Mathematics
Lecturer: As.Prof., PhD. Ukhanska Oksana
Semester: 5 семестр
Mode of study: денна
Learning outcomes: • know the classification problems of mathematical programming; the theoretical foundations of methods of solving linear and nonlinear programming problems; basics of calculus of variations; • be able to construct mathematical models of optimization problems and apply studied methods to find optimal solution applied optimization problems; solve problems using software packages with optimization methods for the PC; • be aware of the main directions of optimization methods and perspectives of practical application of methods of finding the optimal solution.
Required prior and related subjects: • mathematical analysis, • algebra and geometry, • functional analysis, • differential equations, • Programming
Summary of the subject: Construction of mathematical models of linear and non-linear programming problems. Methods for solving of linear and nonlinear programming problems (graphical method, simplex method, modified simplex method, dual simplex method, Gomory method of Lagrange, Kuhn-Tucker theorem). Construction of mathematical models of transportation problems (method of potentials). Elements of the calculus of variations, variation problems on unconditional and conditional extreme functional, direct methods of the calculus of variations.
Assessment methods and criteria: • written reports on laboratory work, oral examination, two tests, two RGR: (45%), • final control (55% of exam), writing (55%)
Recommended books: 1. Цегелик Г.Г. Лінійне програмування. - Львів: Світ, 1995. 2. Барвінський А.Ф., Олексів І.Я. та ін. Математичне програмування. Львів: НУ “ЛП”, 2004. 3. Уханська О.М. Тексти лекцій з курсу ”Методи оптимізації“. – Львів: В-во НУ ”ЛП“, 2003. 4. Эльсгольц Л.Э. Дифференциальные уравнения и вариационное исчисление. – М.: Наука, 1969.