Course detail

Optimization Methods I

FSI-FOA-AAcad. year: 2025/2026

The course introduces students to basic algorithmic approaches for solving various types of optimization problems. The main emphasis is placed on solving continuous deterministic problems (in one or more dimensions) and using the structure of the optimization problem (convexity, linearity, etc.) to apply effective optimization techniques. The conclusion of the course is devoted to advanced methods for solving computationally expensive problems and problems with uncertain data.

Language of instruction

English

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. Ing. Jakub Kůdela, Ph.D.

Department

Institute of Automation and Computer Science (ÚAI)

Entry knowledge

Linear algebra, differential calculus, probability theory, mathematical statistics.

Rules for evaluation and completion of the course

Course-unit credit: Active participation in the seminars, elaboration of a given project. Examination: Written.
Attendance at seminars is controlled. An absence can be compensated for via solving additional problems.

Aims

The emphasis is placed on acquiring application-usable knowledge of methods for solving optimization problems with an emphasis on computer support, implementation, and use of available software.
The student will acquire the skill to recognize a suitable optimization algorithm for a given problem. Furthermore, to implement this algorithm in the selected software and to analyze its behavior.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Boyd, S., Vanderberghe, L.: Convex Optimization. Cambridge University Press, 2004. (EN)
Conforti, M., Cornuéjols, G., Zambelli, G.: Integer Programming. Springer, 2014. (EN)
Kochenderfer, M. J., Wheeler, T. A.: Algorithms for Optimization. MIT Press, 2019. (EN)
Martí, R. Pardalos, P.M., Resende, M.G.C.: Handbook of Heuristics. Springer Cham, 2018. (EN)
Martins, J.R.R.A., Ning. A.: Engineering Design Optimization. Cambridge University Press, 2021. (EN)

Recommended reading

Bazaraa, M. S., Jarvis, J. J., Sherali, H. D.: Linear Programming and Net-work Flows. Wiley, 2009. (EN)
Bazaraa, M. S., Sherali, H. D., Shetty, C. M.: Nonlinear Programming.Wiley, 2006. (EN)
Nocedal, J., Wright, S. J.: Numerical Optimization. Springer, 2006. (EN)
Wolsey, L. A.: Integer Programming. Wiley, 1998. (EN)

Classification of course in study plans

  • Programme N-AIŘ-P Master's 1 year of study, summer semester, compulsory

Type of course unit

 

Lecture

39 hod., optionally

Teacher / Lecturer

doc. Ing. Jakub Kůdela, Ph.D.

Syllabus

1. Introduction to optimization.
2. 1D optimization methods.
3. First and second-order methods.
4. Direct methods and stochastic methods.
5. Population methods, metaheuristics.
6. Convexity theory, KKT conditions, duality.
7. Interior point methods.
8. Linear programming.
9. Simplex method.
10. Integer and combinatorial problems, Branch and bound method, Gomory cuts.
11. Multicriteria optimization.
12. Surrogate-assisted optimization.
13. Optimization under uncertainty.

Exercise

12 hod., compulsory

Teacher / Lecturer

doc. Ing. Jakub Kůdela, Ph.D.

Syllabus

The exercise follows the topics discussed in the lecture. The main focus is on software implementation.

Computer-assisted exercise

14 hod., compulsory

Teacher / Lecturer

doc. Ing. Jakub Kůdela, Ph.D.

Syllabus

The exercise follows the topics discussed in the lecture. The main focus is on software implementation.