Optimization

Relations:

It is not possible to register for the course A4B33OPT if the student is concurrently registered for or has already completed the course AE4B33OPT (mutually exclusive courses).

The requirement for course A4B33OPT can be fulfilled by substitution with the course AE4B33OPT.

It is not possible to register for the course A4B33OPT if the student is concurrently registered for or has previously completed the course AE4B33OPT (mutually exclusive courses).

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Cybernetics

Synopsis:

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.

Requirements:

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

Syllabus of lectures:

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.

Syllabus of tutorials:

The labs consist of solving problems on blackboard and homeworks in Matlab.

Please see the course web page.

Study Objective:

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.

Study materials:

See the course web page.

Note:

Further information:

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

No time-table has been prepared for this course

The course is a part of the following study plans: