# Subject description - B0B33OPT

Summary of Study | Summary of Branches | All Subject Groups | All Subjects | List of Roles | Explanatory Notes               Instructions
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:Cammarata A., 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 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_2016 Common courses P 5 BPKYR_2021 Common courses P 5 BPBIO_2018 Common courses P 5

 Page updated 25.9.2023 15:51:45, semester: Z/2024-5, Z/2023-4, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)