Optimization

Relations:

In order to register for the course B0B33OPT, the student must have registered for the required number of courses in the group BEZBM no later than in the same semester.

Course guarantor:

Tomáš Werner

Lecturer:

Petr Olšák, Tomáš Werner

Tutor:

Jan Čech, Michal Minařík, Petr Olšák, Tomáš Werner

Supervisor:

Department of Cybernetics

Synopsis:

The course provides an introduction to mathematical optimization, specifically to optimization in real vector spaces of finite dimension. The theory is illustrated with a number of examples. You will refresh and extend many topics that you know from linear algebra and calculus courses.

Requirements:

Linear algebra. Calculus, including intro to multivariate calculus. Recommended are numerical algorithms and probability and statistics.

Syllabus of lectures:

1. General problem of continuous optimization.

2. Matrices, linear and affine subspaces, orthogonality.

3. Overdetermined linear systems, least squares.

4. Quadratic forms and functions, definitness of a matrix, spectral decomposition.

5. Singular value decomposition (SVD), application in optimization.

6. Analytical conditions on unconstrained local optima.

7. Iterative methods for unconstrained local optima.

8. Local optima constrained by equalities, Lagrange multipliers.

9. Linear programming - intro.

10. Linear programming - applications.

11. Convex sets and polyhedra.

12. Linear programming - duality.

13. Convex functions.

14. Intro to convex optimization.

Syllabus of tutorials:

At seminars, students exercise the theory by solving problems together using blackboard and solve optimization problems in Matlab as homeworks.

Study Objective:

The aim of the course is to teach students to recognize optimization problems around them, formulate them mathematically, estimate their level of difficulty, and solve easier problems.

Study materials:

Basic:

Online lecture notes Tomáš Werner: Optimalizace (see www pages of the course).

Optionally, selected parts from the books:

Lieven Vandenberghe, Stephen P. Boyd: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares, Cambridge University Press, 2018.

Stephen Boyd and Lieven Vandenberghe: Convex Optimization, Cambridge University Press, 2004. (selected parts)

Note:

Further information:

https://cw.fel.cvut.cz/wiki/courses/B0B33OPT

Time-table for winter semester 2025/2026:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon	roomKN:A-309 09:15–10:45 (lecture parallel1 parallel nr.101) Karlovo nám. roomKN:E-132 11:00–12:30 (lecture parallel1 parallel nr.102) Karlovo nám.
Tue	roomKN:A-310 09:15–10:45 (lecture parallel1 parallel nr.106) Karlovo nám. roomKN:A-309 12:45–14:15 (lecture parallel1 parallel nr.107) Karlovo nám. roomKN:E-107 Werner T. Olšák P. 16:15–17:45 (lecture parallel1) Karlovo nám.
Wed	roomKN:E-132 09:15–10:45 (lecture parallel1 parallel nr.103) Karlovo nám. roomKN:A-309 11:00–12:30 (lecture parallel1 parallel nr.104) Karlovo nám. roomKN:A-310 12:45–14:15 (lecture parallel1 parallel nr.105) Karlovo nám.
Thu
Fri	roomKN:E-107 Werner T. Olšák P. 09:15–10:45 (lecture parallel1) Karlovo nám. roomKN:A-310 11:00–12:30 (lecture parallel1 parallel nr.108) Karlovo nám.

Time-table for summer semester 2025/2026:

Time-table is not available yet

The course is a part of the following study plans:

• Cybernetics and Robotics 2016 (compulsory course in the program)
• Open Informatics - Computer Science 2016 (compulsory course in the program)
• Open Informatics - Internet of Things 2016 (compulsory course in the program)
• Open Informatics - Software 2016 (compulsory course in the program)
• Open Informatics - Computer Games and Graphics 2016 (compulsory course in the program)
• Open Informatics (compulsory course in the program)
• Medical electronics and bioinformatics (compulsory course in the program)
• Open Informatics (compulsory course in the program)
• Open Informatics - Artificial Intelligence and Computer Science 2018 (compulsory course in the program)
• Open Informatics - Internet of Things 2018 (compulsory course in the program)
• Open Informatics - Software 2018 (compulsory course in the program)
• Open Informatics - Computer Games and Graphics 2018 (compulsory course in the program)
• Cybernetics and Robotics 2016 (compulsory course in the program)
• Open Informatics (compulsory course in the program)
• Open Informatics - Artificial Intelligence and Computer Science 2025 (compulsory course in the program)
• Open Informatics - Internet of Things 2025 (compulsory course in the program)
• Open Informatics - Software 2025 (compulsory course in the program)
• Open Informatics - Computer Games and Graphics 2025 (compulsory course in the program)