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.
Language of instruction
English
Number of ECTS credits
5
Supervisor
Department
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.
The study programmes with the given course
Programme N-AIŘ-P: Applied Computer Science and Control, Master's, 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.