Subject description - A4B33OPT

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A4B33OPT Optimization Extent of teaching:4+2c
Guarantors:Werner T. Roles:P,V Language of
Teachers:Kybic J., Werner T. Completion:Z,ZK
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="">lab page </a> for the actual term.


See the course home page


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
BPOI3 Software Systems P 5
BPOI2 Computer and Information Science P 5
BPOI_BO Common courses P 5
BPOI1 Computer Systems P 5
BPKYR_BO Common courses V 5
BPKYR1 Robotics V 5
BPKYR3 Systems and Control V 5
BPKYR2 Sensors and Instrumentation V 5
BPKME1 Communication Technology V 5
BPKME2 Multimedia Technology V 5
BPKME3 Applied Electronics V 5
BPKME4 Network and Information Technology V 5
BPKME_BO Common courses V 5
BPKME5 Komunikace a elektronika V 5
BPEEM1 Applied Electrical Engineering V 5
BPEEM_BO Common courses 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
BWM(ECTS) Web and Multimedia V 5
BIS(ECTS) Intelligent Systems V 5
BSI(ECTS) Software Engineering V 5
BMI(ECTS) Manager Informatics V 5

Page updated 20.6.2018 15:49:10, semester: Z,L/2020-1, L/2019-20, L/2018-9, Z,L/2017-8, Z/2018-9, Z/2019-20, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)