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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:	Olšák P., Werner T.	Credits:	7
Tutors:	Čech J., Minařík M., Olšák P., Werner T.	Semester:	Z,L

Web page:

https://cw.fel.cvut.cz/wiki/courses/B0B33OPT

Anotation:

The course provides an introduction to mathematical optimization, specifically to optimization in real vector spaces of finite dimension. The theory is illustrated with a number of examples. You will refresh and extend many topics that you know from linear algebra and calculus courses.

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.

Literature:

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.

Requirements:

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

Keywords:

matematická optimalizace, lineární programování, nejmenší čtverce, konvexita

Subject is included into these academic programs:

Program	Branch	Role	Recommended semester
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 of Things	P	4
BPBIO_2018	Common courses	P	5
BPOI_BO_2018	Common courses	P	4
BPOI4_2018	Computer Games and Graphics	P	4
BPOI3_2018	Software	P	4
BPOI2_2018	Internet of Things	P	4
BPOI1_2018	Artificial Intelligence and Computer Science	P	4
BPKYR_2021	Common courses	P	5
BPKYR_2016	Common courses	P	5

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Page updated 6.10.2024 17:51:16, semester: Z,L/2024-5, Z/2025-6, L/2023-4, Send comments about the content to the Administrators of the Academic Programs

Proposal and Realization: I. Halaška (K336), J. Novák (K336)