Infopaket

Methods of computational mathematics

ДВС.3.06.01.02

Вибіркова дисципліна для ОП

First

2023/2024

8 Semester

3

LO 1.1 Know the main problems of computational mathematics and approaches to their solution, in particular from the optimal control section LO 1.2 Know the theoretical and practical approaches to the study of optimal control problems for systems with distributed parameters LO 2.1 Be able to find out the issues of solvability for optimal control problems LO 2.2 Be able to implement and research algorithms for computational mathematics problems LO 3.1 Argue one's own choice of approaches to solving a problem, communicate with colleagues on issues of design and program development LO 4.1 Organize your independent work to achieve results LO 4.2 Be responsible for the work performed, bear responsibility for their quality

Full-time form

1. Know: Mathematical analysis, functional analysis, theory of differential equations, theory of optimal control, algebra and numerical methods in the scope of relevant university courses. 2. Be able to: create programs in at least one programming language, read and analyze mathematical texts, implement mathematical algorithms. Read literature in English. 3. Have skills: working with a computer, searching for information on the Internet, using translation tools, creating presentations.

Classical sections of optimization problems. Convex optimization. Optimization problems for systems with distributed parameters. Management options. Theoretical research is the problem of the existence and uniqueness of the solution. General construction approaches and classes of numerical methods for solving optimization problems for systems with distributed parameters. Classical methods of the gradient type for optimization problems and their implementation. Theoretical and practical study of the properties and behavior of numerical methods of the gradient type. Problems with the convergence of methods, ways to solve them.

1. Liashko S.І., Semenov V.V., Kliushin D.A. Spetsіal-nі pitannia optimіzatsії. Kiїv, VPТs “Kiїvs-kii unіversitet”, 2015 2. Vasil-ev F.P. Metody resheniia ekstremal-nykh zadach. – M.: Nauka, 1981. 3. Lyashko S. I. Generalized optimal control of linear systems with distributed parameters. Boston / Dordrecht / London: Kluwer Academic Publishers, 2002. 466 p. 4. Sea Zh. Optimizatsiia. Teoriia i algoritmy. – M.: Mir, 1973. 5. Iosida K. Funktsional-nyi analiz. – M.: Mir, 1967. 6. Nesterov Iu.E. Vvedenie v vypukluiu optimimzatsiiu. – M.: MТsNMO, 2010.

Lectures, laboratory, independent work

- semester assessment: 1. Modular control work - 25 points/15 points 2. Laboratory work 1 – 25 points/15 points 2. Laboratory work 2 – 25 points/15 points 3. Laboratory work 3 – 25 points/15 points - final assessment - credit. Credit is issued based on the results of work in the semester. A student receives a credit if, according to the results of work in the semester, he scored 60 or more points, while successfully writing a modular control paper and at least two laboratory works.

Ukrainian