Optimization

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:

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• Otevřená informatika - Počítačové systémy (compulsory course in the program)
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• Komunikace, multimédia a elektronika, před rozřazením do oborů (elective course)
• Kybernetika a robotika, před rozřazením do oborů (elective course)
• Otevřená informatika, před rozřazením do oborů (compulsory course in the program)
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• Manažerská informatika (STM-A7B-přechodné) (elective course)
• Web a multimedia (STM-A7B-přechodné) (elective course)
• Softwarové inženýrství (STM-A7B-přechodné) (elective course)
• Společný 1.ročník (STM-A7B) (elective course)
• Inteligentní systémy (STM-A7B) (elective course)
• Manažerská informatika (STM-A7B) (elective course)
• Softwarové inženýrství (STM-A7B) (elective course)
• Web a multimedia (STM-A7B) (elective course)