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 Language of
teaching:
CS
Teachers:Kybic J., Werner T. Completion:Z,ZK
Responsible Department:13133 Credits:7 Semester:Z

Anotation:

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.

Literature:

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

Requirements:

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

Webpage:

http://cw.felk.cvut.cz/doku.php/courses/a4b33opt/start

Keywords:

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 12.12.2017 17:48:53, 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.