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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2020/2021

Optimization

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Code Completion Credits Range Language
B0B33OPT Z,ZK 7 4P+2C Czech
Corequisite:
Lecturer:
Tomáš Werner (guarantor), Petr Olšák
Tutor:
Tomáš Werner (guarantor), Jan Čech, Tomáš Dlask, Petr Olšák, Radim Špetlík, Václav Voráček
Supervisor:
Department of Cybernetics
Synopsis:

The course provides the basics of mathematical optimization: using linear algebra for optimization (least squares, SVD), Lagrange multipliers, selected numerical algorithms (gradient, Newton, Gauss-Newton, Levenberg-Marquardt methods), linear programming, convex sets and functions, intro to convex optimization, duality.

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:
http://cw.fel.cvut.cz/wiki/courses/b0b33opt
Time-table for winter semester 2020/2021:
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
Voráček V.
09:15–10:45
(lecture parallel1
parallel nr.101)

Karlovo nám.
Laboratoř PC
roomKN:E-132
Čech J.
11:00–12:30
(lecture parallel1
parallel nr.102)

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

16:15–17:45
(lecture parallel1)
Karlovo nám.
Zengerova posluchárna K1
Fri
roomKN:E-132
Olšák P.
09:15–10:45
(lecture parallel1
parallel nr.103)

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

Karlovo nám.
Laboratoř PC
roomKN:E-132
Dlask T.
12:45–14:15
(lecture parallel1
parallel nr.105)

Karlovo nám.
Laboratoř PC
Thu
roomKN:E-132
Olšák P.
14:30–16:00
(lecture parallel1
parallel nr.106)

Karlovo nám.
Laboratoř PC
room

16:15–17:45
(lecture parallel1
parallel nr.107)

Fri
roomKN:E-107
Werner T.
Olšák P.

09:15–10:45
(lecture parallel1)
Karlovo nám.
Zengerova posluchárna K1
roomKN:E-132
Špetlík R.
11:00–12:30
(lecture parallel1
parallel nr.108)

Karlovo nám.
Laboratoř PC
Time-table for summer semester 2020/2021:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2020-10-30
For updated information see http://bilakniha.cvut.cz/en/predmet4674306.html