Subject description - B0B33OPT

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B0B33OPT Optimization
Roles:P Extent of teaching:4P+2C
Department:13133 Language of teaching:CS
Guarantors:Werner T. Completion:Z,ZK
Lecturers:Kroupa T., Werner T. Credits:7
Tutors:Too many persons Semester:Z,L


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 problem of continuous optimization.
2. Over-determined linear systems, method of least squares.
3. Minimization of quadratic functions.
4. Using SVD in optimization.
5. Algorithms for free local extrema (gradient, Newton, Gauss-Newton, Levenberg-Marquardt methods).
6. Linear programming.
7. Simplex method.
8. Convex sets and polyhedra. Convex functions.
9. Intro to convex optimization.
10. Lagrange formalism, KKT conditions.
11. Lagrange duality. Duality in linear programming.
12. Examples of non-convex problems.
13. Intro to multicriteria optimization.

Exercises outline:

At seminars, students exercise the theory by solving problems together using blackboard and solve optimization problems in Matlab as homeworks.


Basic: Online lecture notes Tomáš Werner: Optimalizace (see www pages of the course). Optionally, selected parts from the books: Lieven Vandenberghe, Stephen P. Boyd: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares, Cambridge University Press, 2018. Stephen Boyd and Lieven Vandenberghe: Convex Optimization, Cambridge University Press, 2004.


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



matematická optimalizace, lineární programování, nejmenší čtverce, konvexita

Subject is included into these academic programs:

Program Branch Role Recommended semester
BPOI_BO_2018 Common courses P 4
BPOI4_2018 Computer Games and Graphics P 4
BPOI3_2018 Software P 4
BPOI2_2018 Internet things P 4
BPOI1_2018 Artificial Intelligence and Computer Science P 4
BPOI1_2016 Computer and Information Science P 4
BPOI_BO_2016 Common courses P 4
BPOI4_2016 Computer Games and Graphics P 4
BPOI3_2016 Software P 4
BPOI2_2016 Internet things P 4
BPBIO_2018 Common courses P 5
BPKYR_2016 Common courses P 5

Page updated 11.8.2020 17:51:51, semester: Z,L/2020-1, L/2019-20, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)