Faculty of Electrical Engineering

Czech Technical University in Prague

CTU in Prague

Subject description - A4B33OPT

Summary of Study | Summary of Branches | All Subject Groups | All Subjects | List of Roles | Explanatory Notes               Instructions
A4B33OPT Optimization Extent of teaching:4+2c
Guarantors:Werner T. Roles:P,V Completion:Z,ZK
Teachers:Kybic J., Werner T.
Responsible Department:13133 Credits:7 Semester:Z


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.

Study targets:

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.

Course outlines:

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.

Exercises outline:

The labs consist of solving problems on blackboard and homeworks in Matlab. Here is <a href="https://cw.felk.cvut.cz/doku.php/courses/a4b33opt/cviceni/start">lab page </a> for the actual term.


See the course home page https://cw.felk.cvut.cz/doku.php/courses/a4b33opt/start


Linear algebra. Calculus, including intro to multivariate calculus. Recommended are numerical algorithms and probability and statistics.




mathematical optimization, linear programming, least squares, convexity

Subject is included into these academic programs:

Program Branch Role Recommended semester
BPOI2 Computer and Information Science P 5
BPOI_BO Common courses P 5
BPOI1 Computer Systems P 5
BPOI3 Software Systems P 5
BPKYR_BO Common courses V 5
BPKYR3 Systems and Control V 5
BPKYR2 Senzors and Instrumention V 5
BPKYR1 Robotics V 5
BPKME5 Komunikace a elektronika V 5
BPKME4 Network and Information Technology V 5
BPKME3 Applied Electronics V 5
BPKME1 Communication Technology V 5
BPKME2 Multimedia Technology V 5
BPKME_BO Common courses V 5
BPEEM_BO Common courses V 5
BPEEM1 Applied Electrical Engineering V 5
BPEEM2 Electrical Engineering and Management V 5
BKSIT Common courses V 5
BPSTMMI Manager Informatics V 5
BPSTMWM Web and Multimedia V 5
BPSIT Common courses V 5
BPSTMSI Software Engineering V 5
BPSTM_BO Common courses V 5
BPSTMIS Intelligent Systems V 5
BIS(ECTS) Intelligent Systems V 5
BSI(ECTS) Software Engineering V 5
BMI(ECTS) Manager Informatics V 5
BWM(ECTS) Web and Multimedia V 5

Page updated 17.10.2017 17:50:50, semester: L/2016-7, Z,L/2017-8, Z/2018-9, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)
Responsible person: doc. Ing. Jiří Jakovenko, Ph.D.