Optimization Methods (курсова робота)

Major: Applied mathematics and computer science
Code of subject: 6.113.01.E.079
Credits: 2.00
Department: Applied Mathematics
Lecturer: As.Prof., PhD. Ukhanska Oksana
Semester: 6 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; 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: • optimization methods, • differential equations, • functional analysis, • Programming.
Summary of the subject: Methods for solving linear and nonlinear programming (Fibonacci method, golden section method, the Ford-Fulkerson algorithm). Construction of mathematical models of transport problems in grid form (method of potentials on the grid). Problems with Boolean variables (Hungarian method, the problem of circular route). Dynamic programming. Elements of the calculus of variations, variation problems in parametric form; n-dimensional variation problems; relationship optimal control problems with the tasks of variations
Assessment methods and criteria: • written course work: (80%), • final control (20%, differentiated test.): oral form (20%)
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. Уханська О.М., Гладун В.Р. Елементи варіаційного числення: посібник. – Львів: Растр-7, 2020. 5. Эльсгольц Л.Э. Дифференциальные уравнения и вариационное исчисление. – М.: Наука, 1969.