Actual problems of applied mathematics

Course: Applied mathematics

Structural unit: Faculty of Computer Science and Cybernetics

Title
Actual problems of applied mathematics
Code
OK.11
Module type
Обов’язкова дисципліна для ОП
Educational cycle
Second
Year of study when the component is delivered
2022/2023
Semester/trimester when the component is delivered
1 Semester
Number of ECTS credits allocated
3
Learning outcomes
PLO1 Possession of in-depth professional knowledge and practical skills to optimize the design of models of any complexity, to solve specific tasks of designing intelligent information systems of various physical nature.
Form of study
Prerequisites and co-requisites
1. Have competence in: Mathematical analysis, functional analysis, theory of differential equations, theory of optimal control, algebra and numerical methods. 2. Be able to: create programs in at least one programming language, read, analyze and write own mathematical texts, implement mathematical algorithms. Confidently read literature in English. 3. Possess skills: working with a computer, searching for information on the Internet, using translation tools, creating mathematical texts and presentations.
Course content
Optimization problems of systems with distributed parameters and singular control. The method of a priori estimates in negative norms. Existence and uniqueness theorems of weak solutions. Methods of approximation of weak solutions. Controllability of systems with distributed parameters and singular control. Schemes for proving the convergence of iterative processes. Conditional gradient method. Convergence and speed estimates. Lower scores for first-order methods. Nesterov's fast gradient method and its modifications. Incorrect tasks. Examples. Correctness according to Tikhonov. The Tikhonov regularization method for optimization problems. Bakushinsky's iterative regularization method. Gradient systems and their application in mathematical programming.
Recommended or required reading and other learning resources/tools
1. Liashko S.І., Sandrakov G.V., Semenov V.V., Kliushin D.A. Matematichne modeliuvannia ta obchisliuval-na matematika. Kiїv, VPТs “Kiїvs-kii unіversitet”, 2020 2. Liashko S.І., Semenov V.V., Kliushin D.A. Spetsіal-nі pitannia optimіzatsії. Kiїv, VPТs “Kiїvs-kii unіversitet”, 2015 3. Sea Zh. Optimizatsiia. Teoriia i algoritmy. – M.: Mir, 1973. 4. Tikhonov A.N., Arsenin V.Ia. Metody resheniia nekorrektnykh zadach. – M.: Nauka, 1979. 5. Gaevskii Kh., Greger K., Zakharias K. Nelineinye operatornye uravneniia i operatornye differentsial-nye uravneniia. – M.: Mir, 1978. 6. Iosida K. Funktsional-nyi analiz. – M.: Mir, 1967. 7. Lyashko S. I. Generalized optimal control of linear systems with distributed parameters. Boston / Dordrecht / London: Kluwer Academic Publishers, 2002. 466 p.
Planned learning activities and teaching methods
Lectures, practical, consultations, independent work
Assessment methods and criteria
- semester assessment: 1. Modular control work 1 – 25 points/15 points 2. Modular control work 2 – 25 points/15 points 3. Report - 25 points/15 points 4. Project – 25 points/15 points - final assessment - credit. Credit is issued based on the results of work in the semester. The student receives a credit if for according to the results of work in the semester, he scored 60 or more points and successfully passed at least two of the three forms of semester control.
Language of instruction
Ukrainian

Lecturers

This discipline is taught by the following teachers

Departments

The following departments are involved in teaching the above discipline