Optimization Methods I (FSI-FOA-A)

Academic year 2025/2026
Supervisor: doc. Ing. Jakub Kůdela, Ph.D.  
Supervising institute: ÚAI all courses guaranted by this institute
Teaching language: English
Aims of the course unit:

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.
Learning outcomes and competences:
 
Prerequisites:
 
Course contents:

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.
Teaching methods and criteria:
 
Assesment methods and criteria linked to learning outcomes:
 
Controlled participation in lessons:
 
Type of course unit:
    Lecture  13 × 3 hrs. optionally                  
    Exercise  6 × 2 hrs. compulsory                  
    Computer-assisted exercise  7 × 2 hrs. compulsory                  
Course curriculum:
    Lecture

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

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

The exercise follows the topics discussed in the lecture. The main focus is on software implementation.
Literature - fundamental:
1. Kochenderfer, M. J., Wheeler, T. A.: Algorithms for Optimization. MIT Press, 2019.
2. Boyd, S., Vanderberghe, L.: Convex Optimization. Cambridge University Press, 2004.
3. Martí, R. Pardalos, P.M., Resende, M.G.C.: Handbook of Heuristics. Springer Cham, 2018.
4. Martins, J.R.R.A., Ning. A.: Engineering Design Optimization. Cambridge University Press, 2021.
5. Conforti, M., Cornuéjols, G., Zambelli, G.: Integer Programming. Springer, 2014.
Literature - recommended:
1. Bazaraa, M. S., Jarvis, J. J., Sherali, H. D.: Linear Programming and Net-work Flows. Wiley, 2009.
2. Bazaraa, M. S., Sherali, H. D., Shetty, C. M.: Nonlinear Programming.Wiley, 2006.
3. Wolsey, L. A.: Integer Programming. Wiley, 1998.
4. Nocedal, J., Wright, S. J.: Numerical Optimization. Springer, 2006.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
N-AIŘ-P full-time study --- no specialisation -- Cr,Ex 5 Compulsory 2 1 S
N-ENG-Z visiting student --- no specialisation -- Cr,Ex 5 Recommended course 2 1 S