Methods of non-smooth optimization

Course: Applied mathematics

Structural unit: Faculty of Computer Science and Cybernetics

Title
Methods of non-smooth optimization
Code
ДВВ.06
Module type
Обов’язкова дисципліна для ОП
Educational cycle
Second
Year of study when the component is delivered
2021/2022
Semester/trimester when the component is delivered
2 Semester
Number of ECTS credits allocated
3
Learning outcomes
PLO7. Be able to organize, configure, and develop web systems using the principles of distributed systems, hypertext systems, and appropriate hardware and software.
Form of study
Full-time form
Prerequisites and co-requisites
To successfully study the discipline "Non-smooth optimization methods", a student must meet the following requirements: 1. Mastering the competencies of the disciplines: 1. Mathematical analysis. 2. Functional analysis. 3. Operations research. 4. Management theory. 2. Knowledge: 1. Theoretical foundations and methods of system research using the approaches of functional analysis, operations research, and control theory. 2. Principles of building systems. 3. Skill: 1. Solve the basic problems of operations research and management theory. 2. Solve basic problems of mathematical analysis. 3. Formulate optimization problems for solving practical problems. 4. Apply methods of mathematical and computer modeling to study systems and build mathematical models. 4. Ownership: 1. Programming skills. 2. Skills in construction, analysis, and application of mathematical models when solving applied problems of non-smooth analysis.
Course content
Familiarization with the methods of differentiating non-smooth functions, numerical methods for solving optimization problems with a non-differentiable quality criterion, and methods for solving optimal control problems with a non-smooth quality criterion. The course includes two tests. The discipline ends with a test.
Recommended or required reading and other learning resources/tools
1. Bashniakov O.M., Harashchenko F.H., Pichkur V.V. Praktychna stiikist, otsinky ta optymizatsiia. – K.: Kyivskyi universytet. – 2008. 2. Nesterov Y. Lectures on Convex Optimization. – Springer, 2018. – 603 p. 3. Mokliachuk M.P. Nehladkyi analiz ta optymizatsiia. K.: Kyivskyi universytet, 2008. 4. Pichkur V. V., Kapustian O. V., Sobchuk V. V. Teoriia dynamichnykh system. – Lutsk : Vezha-Druk, 2020. – 348 p. 5. Mokliachuk M.P. Variatsiine chyslennia. Ekstremalni zadachi. – K.: Lybid, 1994. 6. Shor N.Z. Metodi minimizatsii nedifferentsiruemikh funktsii i ikh prilozhenie. – K.: Naukova dumka, 1979. 7. Bashniakov O.M., Pichkur V.V. Zadacha syntezu v teorii keruvannia: Navchalnyi posibnyk. – K.: Vyd-vo «Stal», 2012. – 116 p.
Planned learning activities and teaching methods
Lectures, independent work.
Assessment methods and criteria
Semester evaluation: The maximum number of points that can be received by a student is 100 points. 1. Control work No. 1: 30/18 points. 2. Control work No. 2: 30/18 points. 3. Independent work No. 1: 20/12 points. 4. Current evaluation: 20/12 points. Final evaluation (credit): According to paragraphs 4.6.1 and 7.1.5 "Regulations on the organization of the educational process at the Taras Shevchenko National University of Kyiv" credit is given based on current control (see semester evaluation) as the sum of grades/points for all successfully evaluated learning outcomes; grades below the minimum threshold level of the final grade are not added. All students are allowed to take the test.
Language of instruction
Ukrainian

Lecturers

This discipline is taught by the following teachers

Andrii Leonidovych Maksymenko
Complex systems modelling
Faculty of Computer Science and Cybernetics

Departments

The following departments are involved in teaching the above discipline

Complex systems modelling
Faculty of Computer Science and Cybernetics