CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2018/2019

# Optimization

Code Completion Credits Range Language
A4B33OPT Z,ZK 7 4+2c Czech
The course cannot be taken simultaneously with:
Optimization (AE4B33OPT)
Lecturer:
Tomáš Werner (guarantor), Zuzana Kúkelová
Tutor:
Tomáš Werner (guarantor), Tomáš Jeníček, Zuzana Kúkelová
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 formulation of continuous optimization problems.

2. Matrix algebra. Linear and affine subspaces and mappings.

3. Orthogonality. QR decomposition.

4. Non-homogeneous linear systems: method of least squares and least norm.

6. Singular value decomposition (SVD).

7. Non-linear mappings, their derivatives.

8. Analytical conditions on free extrema. Method of Lagrange multipliers.

10. Linear programming: formulation and applications.

11. Convex sets and polyhedra.

12. Simplex method.

13. Duality in linear progrmaming.

14. Convex functions. Convex optimization problems.

15. Examples of non-convex problems.

Syllabus of tutorials:

The labs consist of solving problems on blackboard and homeworks in Matlab.

Please see the course web page.

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:

See the course web page.

Note:
Further information:
http://cw.felk.cvut.cz/doku.php/courses/b33opt/start
Time-table for winter semester 2018/2019:
 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-132Jeníček T.18:00–19:30(lecture parallel1parallel nr.101)Karlovo nám.Laboratoř PC roomKN:E-107Werner T.Kúkelová Z.16:15–17:45(lecture parallel1)Karlovo nám.Zengerova posluchárna K1 roomKN:E-107Werner T.Kúkelová Z.09:15–10:45(lecture parallel1)Karlovo nám.Zengerova posluchárna K1
Time-table for summer semester 2018/2019:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2019-05-23
For updated information see http://bilakniha.cvut.cz/en/predmet12581504.html