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Nonclassical optimal control problems

Вибіркова дисципліна для ОП

Second

2021/2022

3 Semester

8

PLO13.1. Be able to use professional knowledge, skills and abilities in the field of computational mathematics and computer science to model real processes of different nature.

Know the basic concepts and facts of mathematical analysis, functional analysis and theory of differential equations. Be able to solve typical problems in mathematical analysis, functional analysis and differential equations. Have basic skills of searching for information on the Internet.

Students should gain basic knowledge of pulse-point control of distributed systems and modern algorithms of convex programming. This knowledge will help to apply modern methods to solve problems of optimal control, operations research, building mathematical models. The student who has studied the course will be guided in the modern scientific literature on the range of issues.

Semenov VV, Variational inequalities: theory and algorithms. Kyiv: VPC "Kyiv University", 2021. Nurminsky E. A. Numerical methods for solving deterministic and stochastic minimax problems. Kiev: Nauk. Dumka, 1979. Kinderlehrer D., Stampacchia G. Introduction to variational inequalities and their applications. Moscow: Mir, 1983. Nesterov Yu. E. Introduction to convex optimization. Moscow: MCNMO, 2010. Lyashko S. I. Generalized optimal control of linear systems with distributed parameters. Boston-Dordrecht-London: Kluwer Academic Publishers, 2002. Beck A. First-Order Methods in Optimization. Philadelphia: Society for Industrial and Applied Mathematics, 2017. Bauschke H. H., Combettes P. L. Convex Analysis and Monotone Operator Theory in Hilbert Spaces. Springer, 2011.

Lectures, independent work, recommended literature processing, homeworks, test works.

Maximum number of points that can be obtained by a student: 100 points. - Intermediate assessment: Test work 1: LO 1.1, LO 1.2, LO 2.1 - 40 points / 24 points. Test work 2: LO 1.1, LO 1.2, LO 2.1 - 40 points / 24 points. Current assessment in lectures: LO 1.1, LO 1.2, LO 2.1, LO 3.1, LO 4.1, LO 4.2 - 20 points. - Final assessment: the test is based on the results of the student's work throughout the semester and does not provide additional assessment activities for successful students. - conditions of admission to the final test: it is necessary to successfully write tests.

Ukrainian