Applications of Optimization Methods

Course guarantor:

Tomáš Oberhuber

Lecturer:

Tomáš Oberhuber

Tutor:

Tomáš Oberhuber

Supervisor:

Department of Mathematics

Synopsis:

Aim of this course is to enhance the knowledge of the optimization methods and show their practical applications. Number

of methods are applied on the support-vector machines and subsequently, methods for large problems and training of deep

artificial neural networks are explained. Finaly, advanced methods for regret minimization or sparsity inducing methods

are explained. All methods are demonstrated on real problems.

Requirements:

Syllabus of lectures:

1. Introduction to advanced optimization methods.

2. Support-vector mechines.

3. Artificial neural networks in optimization.

4. Hessian inverse approximation, BFGS method.

5. Stochastic gradient descent.

6. Convex optimizations for regret minimization.

7. Sparsity-inducing optimization methods.

Syllabus of tutorials:

Study Objective:

Study materials:

Compulsory literature:

[1] H. J. Kochenderfer, T. A. Wheeler, Algorithms for Optimization, The MIT Press, 2019.

[2] S. Sra, S. Nowozin, S. J. Wright, Optimization for Machine Learning, The MIT Press, 2012.

[3] D. P. Bertsekas, Convex Optimization Algorithms, Athena Scientific, 2015.

Optional literature:

[5] I. Goodfellow, Y. Bengio, A. Courville, Deep Learning, The MIT Press, 2016.

[6] Ch. C. Aggarwal, Neural Networks and Deep Learning, Springer, 2018.

Note:

Time-table for winter semester 2024/2025:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon	roomTR:105 Oberhuber T. 10:00–11:50 (lecture parallel1) Trojanova 13
Tue
Wed
Thu
Fri

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Aplikace informatiky v přírodních vědách (elective course)
• Matematické inženýrství (compulsory course in the program)