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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2024/2025
NOTICE: Study plans for the following academic year are available.

Optimization

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Code Completion Credits Range Language
B0B33OPT Z,ZK 7 4P+2C Czech
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:
Tomáš Kroupa, Mirko Navara, Petr Olšák, Tomáš Werner
Tutor:
Jan Čech, Ondřej Drbohlav, Tomáš Kroupa, Michal Minařík, Mirko Navara, Petr Olšák, Kateřina Poláková, 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
Mon
roomKN:E-132
Čech J.
09:15–10:45
(lecture parallel1
parallel nr.101)

Karlovo nám.
roomKN:E-132
Olšák P.
11:00–12:30
(lecture parallel1
parallel nr.102)

Karlovo nám.
roomKN:E-230

09:15–10:45
(lecture parallel1
parallel nr.107)

Karlovo nám.
Tue
roomKN:E-107
Werner T.
Olšák P.

16:15–17:45
(lecture parallel1)
Karlovo nám.
Wed
roomKN:E-132
Olšák P.
09:15–10:45
(lecture parallel1
parallel nr.103)

Karlovo nám.
roomKN:E-132
Olšák P.
11:00–12:30
(lecture parallel1
parallel nr.104)

Karlovo nám.
roomKN:E-132
Minařík M.
12:45–14:15
(lecture parallel1
parallel nr.105)

Karlovo nám.
Thu
roomKN:E-230

14:30–16:00
(lecture parallel1
parallel nr.106)

Karlovo nám.
Fri
roomFS_KN:A-320
Werner T.
Olšák P.

09:15–10:45
(lecture parallel1)
Karlovo nám.
roomKN:E-132

11:00–12:30
(lecture parallel1
parallel nr.108)

Karlovo nám.
roomKN:E-107
Werner T.
Olšák P.

09:15–10:45
(lecture parallel1)
Karlovo nám.
Time-table for summer 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
Mon
roomKN:A-309
Minařík M.
09:15–10:45
(lecture parallel1
parallel nr.101)

Karlovo nám.
Tue
roomKN:A-309
Drbohlav O.
09:15–10:45
(lecture parallel1
parallel nr.102)

Karlovo nám.
Wed
roomKN:A-309
Olšák P.
09:15–10:45
(lecture parallel1
parallel nr.103)

Karlovo nám.
roomKN:A-309
Olšák P.
11:00–12:30
(lecture parallel1
parallel nr.106)

Karlovo nám.
roomKN:E-107
Kroupa T.
Navara M.

14:30–16:00
(lecture parallel1)
Karlovo nám.
roomKN:A-420
Poláková K.
09:15–10:45
(lecture parallel1
parallel nr.105)

Karlovo nám.
Thu
roomKN:A-309
Drbohlav O.
09:15–10:45
(lecture parallel1
parallel nr.107)

Karlovo nám.
roomKN:A-309
Drbohlav O.
11:00–12:30
(lecture parallel1
parallel nr.108)

Karlovo nám.
Fri
roomKN:E-107
Kroupa T.
Navara M.

09:15–10:45
(lecture parallel1)
Karlovo nám.
roomKN:A-309

11:00–12:30
(lecture parallel1
parallel nr.104)

Karlovo nám.
The course is a part of the following study plans:
Data valid to 2025-04-07
For updated information see http://bilakniha.cvut.cz/en/predmet4674306.html