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Actual problems of applied mathematics

OK.11

Обов’язкова дисципліна для ОП

Second

2023/2024

1 Semester

3

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.

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.

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.

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.

Lectures, practical, consultations, independent work

- 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.

Ukrainian