Optimization of complex systems (am 1,4)
Type: Normative
Curriculum
| Semester | Credits | Reporting |
| 11 | 3 | Exam |
Lectures
| Semester | Amount of hours | Lecturer | Group(s) |
| 11 | 16 | Associate Professor M. V. Shcherbatyy | PMp-61m |
Laboratory works
| Semester | Amount of hours | Group | Teacher(s) |
| 11 | 16 | PMp-61m | Associate Professor M. V. Shcherbatyy, Associate Professor, Senior Researcher V. M. Kukharskyy |
Course description
Brief abstract of the discipline
This course concerns optimization problems of complex systems, governed by ordinary differential equations and partial differential equations. Numerical methods for solution of optimization problems, which are based on direct and indirect approaches, are considered. Sensitivity analysis relations in discrete formulation that are obtained using various methods are presented. First-order necessary optimality conditions for finite-dimensional controls are obtained. A number of applications examples from different fields illustrate the material of this course.
Recommended Literature
Basic literature
1. F. Tröltzsch. Optimal Control of Partial Differential Equations (Graduate Studies in Mathematics). AMS, 2010.
2. M. Hinze, R. Pinnau, M. Ulbrich, S. Ulbrich. Optimization with PDE Constraints. Springer, 2009.
3. Reyes J.C. Numerical PDE-Constrained Optimization. Springer, 2015.
4. Borzi A., Modelling with Ordinary Differential Equations. A Comprehensive Approach. CRC Press, 2020.
5. Arora J.S., Introduction to Optimum Design. Elsevier Inc., 2017.
Additional literature
6. Choi K. K., Kim N. H. Structural Sensitivity Analysis and Optimization 1. Linear Systems. Springer, 2005.
7. Speyer J. L., Jacobson D. H., Primer on optimal control theory. SIAM, 2010.
8. Shcherbatyy M.V. Sensitivity analysis for one-dimensional semilinear partial differential equations. // Вісник Київського національного університету імені Тараса Шевченка, Серія: фізико-математичні науки. – 2017. – №2. – С. 157-164.
9. Наконечний О.Г. Оптимальне керування та оцінювання в рівняннях із частинними похідними.: Навчальний посібник. К.: ВПЦ “Київський університет”, 2004.
10. Бейко І.В., Зінько П.М., Наконечний О.Г. Задачі, методи і алгоритми оптимізації. Навчальний посібник. Рівне, 2011.
11. MATLAB Homepage: http://www.mathworks.com/products/matlab/.
12. GNU Octave Homepage: http://www.gnu.org/software/octave/