# Subject description - A4B33OPT

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 A4B33OPT Optimization Extent of teaching: 4P+2C Guarantors: Roles: P,V Language ofteaching: CS Teachers: Completion: Z,ZK Responsible Department: 13133 Credits: 7 Semester: Z

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 formulation of continuous optimization problems. 2 Matrix algebra. Linear and affine subspaces and mappings. 3 Orthogonality. QR decomposition. 4 Non-homogeneous linear systems: method of least squares and least norm. 5 Quadratic functions, spectral decomposition. 6 Singular value decomposition (SVD). 7 Non-linear mappings, their derivatives. 8 Analytical conditions on free extrema. Method of Lagrange multipliers. 9 Iterative algorithms for free local extrema: gradient, Newton, Gauss-Newton, Levenberg-Marquard method. 10 Linear programming: formulation and applications. 11 Convex sets and polyhedra. 12 Simplex method. 13 Duality in linear progrmaming. 14 Convex functions. Convex optimization problems. 15 Examples of non-convex problems.

Exercises outline:

The labs consist of solving problems on blackboard and homeworks in Matlab. Please see the course web page.

Literature:

See the course web page.

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:

mathematical optimization, linear programming, least squares, convexity

Subject is included into these academic programs:

 Program Branch Role Recommended semester BPOI1 Computer Systems P 5 BPOI_BO Common courses P 5 BPOI3 Software Systems P 5 BPOI2 Computer and Information Science P 5 BPKYR1 Robotics V 5 BPKYR_BO Common courses V 5 BPKYR3 Systems and Control V 5 BPKYR2 Sensors and Instrumentation V 5 BPKME1 Communication Technology V 5 BPKME5 Komunikace a elektronika V 5 BPKME_BO Common courses V 5 BPKME4 Network and Information Technology V 5 BPKME3 Applied Electronics V 5 BPKME2 Multimedia Technology V 5 BPEEM1 Applied Electrical Engineering V 5 BPEEM_BO Common courses V 5 BPEEM2 Electrical Engineering and Management V 5 BMI(ECTS) Manager Informatics V 5 BWM(ECTS) Web and Multimedia V 5 BIS(ECTS) Intelligent Systems V 5 BSI(ECTS) Software Engineering V 5

 Page updated 21.2.2020 17:51:44, semester: Z,L/2020-1, 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)