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. Over-determined linear systems, method of least squares.

3. Minimization of quadratic functions.

4. Using SVD in optimization.

5. Algorithms for free local extrema (gradient, Newton, Gauss-Newton, Levenberg-Marquardt methods).

6. Linear programming.

7. Simplex method.

8. Convex sets and polyhedra. Convex functions.

9. Intro to convex optimization.

10. Lagrange formalism, KKT conditions.

11. Lagrange duality. Duality in linear programming.

12. Examples of non-convex problems.

13. Intro to multicriteria 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.

Note:

Further information:

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

Time-table for winter semester 2025/2026:

Time-table is not available yet

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)