Course detail

Optimization Methods I

FSI-FOA-A Acad. year: 2025/2026 Summer semester

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.

Learning outcomes of the course unit

Prerequisites

Planned learning activities and teaching methods

Assesment methods and criteria linked to learning outcomes

Language of instruction

English

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.

Specification of controlled education, way of implementation and compensation for absences

The study programmes with the given course

Programme N-AIŘ-P: Applied Computer Science and Control, Master's
branch ---: no specialisation, 5 credits, compulsory

Type of course unit

 

Lecture

39 hours, optionally

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 hours, compulsory

Syllabus

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

Computer-assisted exercise

14 hours, compulsory

Syllabus

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