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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:	Navara M., Olšák P., Werner T.	Credits:	7
Tutors:	Too many persons	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.		Matrices, linear and affine subspaces, orthogonality.
3.		Overdetermined linear systems, least squares.
4.		Quadratic forms and functions, definitness of a matrix, spectral decomposition.
5.		Singular value decomposition (SVD), application in optimization.
6.		Analytical conditions on unconstrained local optima.
7.		Iterative methods for unconstrained local optima.
8.		Local optima constrained by equalities, Lagrange multipliers.
9.		Linear programming - intro.
10.		Linear programming - applications.
11.		Convex sets and polyhedra.
12.		Linear programming - duality.
13.		Convex functions.
14.		Intro to convex 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. (selected parts)

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
BPKYR_2021	Common courses	P	5
BPBIO_2018	Common courses	P	5
BPKYR_2016	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
BPBIO_2026	Common courses	P	5
BPOI_BO_2025	Common courses	P	4
BPOI4_2025	Computer Games and Graphics	P	4
BPOI3_2025	Software	P	4
BPOI2_2025	Internet of Things	P	4
BPOI1_2025	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 of Things	P	4

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Page updated 14.5.2026 17:52:36, semester: Z,L/2027-8, Z/2028-9, L/2029-30, L/2028-9, Z,L/2025-6, Z,L/2026-7, Send comments about the content to the Administrators of the Academic Programs

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