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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

Optimization

The course is not on the list Without time-table
Code Completion Credits Range Language
AD4B33OPT Z,ZK 7 28KP+6KC Czech
Lecturer:
Tutor:
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.

5. Quadratic functions, spectral decomposition.

6. Singular value decomposition (SVD).

7. Non-linear mappings, their derivatives.

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

9. Iterative algorithms for free local extrema: gradient, Newton, Gauss-Newton, Levenberg-Marquard method.

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
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2019-10-15
For updated information see http://bilakniha.cvut.cz/en/predmet1206306.html