Infopaket

Theory of optimization in functional spaces

OK.16

Обов’язкова дисципліна для ОП

Second

2023/2024

1 Semester

3

PLO 8. Communicate effectively about information, ideas, problems and solutions with specialists and society in general.

1. Have competence 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. 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.

Problems of calculus of variations and optimal control. Compactness in metric and topological spaces. Semi-continuous functions. Existence theorems. Convex sets. Separability theorems. Convex, strictly and strongly convex functions. Elements of differential calculus in Banach spaces. Derivatives of Gato, Fréchet. Conditions of optimality. Variational inequalities. Control work 2 Discretization of calculus of variations and optimal control problems. Scheme of Nurminsky's proof of convergence of iterative processes. Gradient descent method. Convergence theorems. Conditional gradient method. Convergence theorems. Problems of optimization of systems with distributed parameters. The method of a priori estimates in negative norms. Control regularization in impulse-point control problems.

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. Vasil-ev F. P. Chislennye metody resheniia ekstremal-nykh zadach. M.: Nauka, 1988 4. Nurminskii E. A. Chislennye metody resheniia determinirovannykh i stokhasticheskikh minimaksnykh zadach. Kiev: Nauk. dumka, 1979 5. Lyashko S. I. Generalized optimal control of linear systems with distributed parameters. Boston / Dordrecht / London: Kluwer Academic Publishers, 2002. 466 p. 6. Liashko S. I., Nomirovskii D. A., Petunin Iu. I., Semenov V. V. Dvadtsataia problema Gil-berta. Obobshchennye resheniia operatornykh uravnenii. M.: OOO I. D. Vil-iams, 2009

Lectures, practical, consultations, independent work

- semester assessment: 1. Modular control work 1 – 20 points/12 points 2. Modular control work 2 – 20 points/12 points 3. Report – 20 points/12 points - final evaluation (in the form of an exam): - the maximum number of points that can be obtained by a student: 40 points; - learning outcomes that will be assessed: PH1.1, PH1.2, PH1.3, PH2.2; - form of implementation and types of tasks: written. Types of tasks: 4 written tasks - two theoretical questions and two tasks on relevant topics. Each task is valued at 10 points.

Ukrainian