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Theory of optimization in functional spaces

Обов’язкова дисципліна для ОП

Second

2023/2024

1 Semester

3

PLO8. Communicate effectively on information, ideas, problems and solutions with professionals and society at large.

1. Have competencies in: Mathematical analysis, functional analysis, theory of differential equations, theory of optimal control, algebra and numerical methods. 2. Be able to: read, understand, analyze and create mathematical texts. Be skilled at reading literature in English. 3. Have skills: working with a computer, searching for information on the Internet, using translation tools, creating mathematical texts and presentations.

The purpose of the discipline - in-depth acquaintance of students with modern approaches to mathematical research in the field of control theory and optimization. Preparing students for independent research in the relevant sections of applied mathematics. Within the discipline, students gain knowledge about the current state of research in mathematical control theory, master research techniques using a powerful tools of functional analysis, in particular, learn to work in Sobolev spaces, prove a priori inequalities in negative norms for generalized functions and more. Students also practice in conducting and presenting research results.

1.Lyashko S.I., Sandrakov H.V., Semenov V.V., Klyushin D.A. Matematychne modeliuvannia ta obchysliuvalna matematyka. Kyiv, VPTs “Kyivskyi universytet”, 2020 2.Lyashko S.I., Semenov V.V., Klyushin D.A. Spetsialni pytannia optymizatsii. Kyiv, VPTs “Kyivskyi universytet”, 2015 3.Vasylev F. P. Chyslennie metody resheniya ekstremalnykh zadach. M.: Nauka, 1988 4.Nurmynskyi E. A. Chyslennye metody reshenyia determynyrovannykh i stokhastycheskykh mynymaksnykh zadach. Kyev: Nauk. dumka, 1979 5.Lyashko S. I. Generalized optimal control of linear systems with distributed parameters. Boston/Dordrecht/London: Kluwer Academic Pubs, 2002 6.Lyashko S. Y., Nomyrovskyi D. A., Petunyn Yu. Y., Semenov V. V. Dvadtsataia problema Hylberta. Obobshchennye reshenyia operatornykh uravnenyi. M.: OOO Y. D. Vyliams, 2009 ..

Lectures, seminars, independent work, homework tasks.

- semester assessment: 1. Test 1 - 20 points / 12 points 2. Test 2 - 20 points / 12 points 3. Report presentation - 20 points / 12 points - final assessment (in the form of an exam): - the maximum number of points that can be obtained by a student: 40 points; - form: written. Types of tasks: 4 written tasks - two theoretical questions and two tasks on relevant topics. Each task is worth 10 points. Evaluation organization: 1. Test 1: up to 8 week of the semester. 2. Report presentation: up to 12 week of the semester. 3. Test 2: until the end of the semester.

Ukrainian