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Methods of non-smooth optimization

ОК.18

Обов’язкова дисципліна для ОП

Second

2023/2024

2 Semester

3

PLO7. Be able to organize, configure, and develop web systems using the principles of distributed systems, hypertext systems, and appropriate hardware and software.

Full-time form

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.

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.

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.

Lectures, independent work.

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.

Ukrainian