Computing Methods in Optimization Problems (FSI-VOU-A)

Academic year 2025/2026
Supervisor: doc. Ing. Jakub Kůdela, Ph.D.  
Supervising institute: ÚAI all courses guaranted by this institute
Teaching language: English
Course type: departmental course
Aims of the course unit:
 
Learning outcomes and competences:
 
Prerequisites:
 
Course contents:
 
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Assesment methods and criteria linked to learning outcomes:

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.
Controlled participation in lessons:
 
Type of course unit:
    Lecture  13 × 2 hrs. optionally                  
    Computer-assisted exercise  13 × 3 hrs. compulsory                  
Course curriculum:
    Lecture 1. Introduction to optimization (basic concepts).
2. Software tools for optimization: languages/enviroments: EXCEL, MATLAB, Julia. The use of solvers.
3. - 5. Optimization problems in engineering, types of optimization models (linear, quadratic, convex, etc.)
6. - 7. Integer programming problems – applications in logistics, scheduling, etc.
8. Linearization, modelling with SOS1 and SOS2 variables.
9. Black-box optimization and optimization within a simulation environment.
10. Dynamic optimization models.
11. - 13. Models with uncertain data – stochastic and robust formulations.
    Computer-assisted exercise The exercise follows the topics discussed in the lecture. The main focus is on software implementation.
Literature - fundamental:
1. Williams, H.P. Model Building in Mathematical Programming, 4th edition. J.Wiley and Sons, 2012.
2. Hurlimann, T.: Mathematical Modeling Basics, 1st edition. University of Fribourg, 2024.
3. Rardin, R.L.: Optimization in Operations Research, 2nd edition. Pearson Higher Education, 2017.
Literature - recommended:
1. Boyd, S.P. a Vandenberghe, L. Convex Optimization, Cambridge University Press, 2004.
2. Bazaraa, M. S., Jarvis, J. J., Sherali, H. D.: Linear Programming and Net-work Flows. Wiley, 2009.
3. Wolsey, L. A.: Integer Programming. Wiley, 1998.
4. Kochenderfer, M. J., Wheeler, T. A.: Algorithms for Optimization. MIT Press, 2019.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
C-AKR-P full-time study CLS -- Cr,Ex 7 Elective 1 1 S
B-STR-P full-time study AIŘ Applied Computer Science and Control -- Cr,Ex 7 Compulsory 1 3 S