# Subject description - B0B33OPT

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 B0B33OPT Optimization Extent of teaching: 4P+2C Guarantors: Werner T. Roles: P Language ofteaching: CS Teachers: Kroupa T., Werner T. Completion: Z,ZK Responsible Department: 13133 Credits: 7 Semester: Z,L

Anotation:

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.

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.

Webpage:

http://cw.felk.cvut.cz/doku.php/courses/b33opt/start

Keywords:

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 5 BPOI4_2018 Computer Games and Graphics P 5 BPOI3_2018 Software P 5 BPOI2_2018 Internet things P 5 BPOI1_2018 Artificial Intelligence and Computer Science P 5 BPOI1_2016 Computer and Information Science P 5 BPOI_BO_2016 Common courses P 5 BPOI4_2016 Computer Games and Graphics P 5 BPOI3_2016 Software P 5 BPOI2_2016 Internet things P 5 BPBIO_2018 Common courses P 5 BPKYR_2016 Common courses P 5

 Page updated 14.10.2019 17:53:36, semester: Z,L/2020-1, L/2018-9, Z,L/2019-20, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)