CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2024/2025

# Selected Topics in Optimization and Numerical mathematics

The course is not on the list Without time-table
Code Completion Credits Range Language
NI-PON Z,ZK 5 2P+1C Czech
Garant předmětu:
Lecturer:
Tutor:
Supervisor:
Department of Applied Mathematics
Synopsis:

The course focuses on optimization problems that appear in the field of machine learning and artificial intelligence. Students broaden their knowledge of continuous optimization obtained in the course Mathematics for informatics. The methods are explained and described along with the details on how they are implemented on computers. Hence, the relevant concepts of numerical matematics, mainly numerical linear algebra, are explained too.

Requirements:

NIE-MPI

Syllabus of lectures:

1. Continuous optimization: problem statement and machine learning examples.

2. - 3. (2) Iterative methods for finding local extremal values (gradient descent, Newton's method, and their variants).

4. Lagrange method, Karush–Kuhn–Tucker conditions.

5. Duality and interior point method.

6. - 7. (2) QR decomposition, algorithms computing QR decomposition, QR algorithm.

8. - 9. (2) Linear regression and least squares method: statistical and numerical properties.

10. - 11. (2) Support Vector Machines regression.

12. - 13. (2) Matrix factorizations and their usage in machine learning (SVD, PCA, non-negative factorization).

Syllabus of tutorials:

1. Iterative methods for local extrema

2. Constrained optimization

3. Duality

4. Matrix factorizations

5. SVD, PCA

6. SVM

Study Objective:
Study materials:

1. Christopher Bishop, Pattern Recognition and Machine Learning, Springer-Verlag New York, 2006

2. Trevor Hastie, Robert Tibshirani, Jerome Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer, 2011.

3. Stephen Boyd, Lieven Vandenberghe, Convex Optimization, Cambridge University Press, 2004.

4. Lloyd N. Trefethen, David Bau, Numerical Linear Algebra, SIAM: Society for Industrial and Applied Mathematics, 1997

Note:
Further information:
https://courses.fit.cvut.cz/NI-PON
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2024-06-16
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