CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2024/2025

# Optimization

Code Completion Credits Range Language
B0B33OPT Z,ZK 7 4P+2C Czech
Vztahy:
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.
Garant předmětu:
Tomáš Werner
Lecturer:
Petr Olšák, Tomáš Werner
Tutor:
Antonio Cammarata, 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 2024/2025:
 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 roomKN:E-13209:15–10:45(lecture parallel1parallel nr.101)Karlovo nám.Laboratoř PCroomKN:E-13211:00–12:30(lecture parallel1parallel nr.102)Karlovo nám.Laboratoř PC roomKN:E-23009:15–10:45(lecture parallel1parallel nr.107)Karlovo nám.Laboratoř PC roomKN:E-107Werner T.Olšák P.16:15–17:45(lecture parallel1)Karlovo nám.Zengerova posluchárna K1 roomKN:E-13209:15–10:45(lecture parallel1parallel nr.103)Karlovo nám.Laboratoř PCroomKN:E-13211:00–12:30(lecture parallel1parallel nr.104)Karlovo nám.Laboratoř PCroomKN:E-13212:45–14:15(lecture parallel1parallel nr.105)Karlovo nám.Laboratoř PC roomKN:E-23014:30–16:00(lecture parallel1parallel nr.106)Karlovo nám.Laboratoř PC roomKN:E-107Werner T.Olšák P.09:15–10:45(lecture parallel1)Karlovo nám.Zengerova posluchárna K1roomKN:E-13211:00–12:30(lecture parallel1parallel nr.108)Karlovo nám.Laboratoř PC
Time-table for summer semester 2024/2025:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-06-16
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet4674306.html