Optimization for Scientific Computing

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Applied Mathematics

Synopsis:

The content of the course is an explanation of numerical methods for solving nonlinear optimization, convex optimization, stochastic optimization, optimal control, applications for QC, genetic and evolutionary programming, machine learning, deep neural networks. Students are also introduced to modern trends in solving these problems.

Requirements:

Syllabus of lectures:

1.Optimization problems, genetic algorithms and their variants.

2. The annealing method, the flock method.

3. Multi-criteria optimization, Pareto set.

4. Visualization of multidimensional Pareto sets, Taguchi method, evolutionary programming.

5. Machine learning methods - traditional approaches.

6. Machine learning methods - deep learning.

7. Data-driven models and evolutionary programming.

8. QC optimization algorithms.

9. Optimal control - Pontrjagin's maximum principle.

10. Optimal control - Bellman's optimality principle, Bellman's differential equation.

11. Dynamic programming, stochastic and bionic solution methods.

12. Optimization for partial differential equations - general principles.

13. Optimization for partial differential equations - applications.

Syllabus of tutorials:

Not filled yet.

Study Objective:

The content of the course is an explanation of numerical methods for solving nonlinear optimization, convex optimization, stochastic optimization, optimal control, applications for QC, genetic and evolutionary programming, machine learning, deep neural networks. Students are also introduced to modern trends in solving these problems.

Study materials:

1. Kalyanmoy Deb: Multi-Objective Optimization using Evolutionary Algorithms

Wiley 2001, ISBN 978-0-471-87339-6

2. Chakraborti, N.:Data-driven evolutionary modeling in materials technology

Taylor&Francis 2022, ISBN 9781003201045

3. Prakash, S. Y., Prasad, D. M., Nguyen, T. D. L. (eds.:Distributed Artificial Intelligence)

CRC Press 2021, ISBN 9781003038467

4. Goodfellow, I., Bengio, Y., Courville, A.: Deep Learning

MIT Press 2016, ISBN 0262035618

5. Wang, Y., Kim, J. E., Suresh, K.: Opportunities and Challenges of Quantum Computing for Engineering Optimization,

ASME J. of Computing and Information Science in Engineering 2023, ISBN 060817-1-8

6. Lewis, F. L., Vrabie, D. L., Syrmos, V. L.: Optimal Control

Wiley 2012, , ISBN 9780470633496

7. Roubicek, T.: Relaxation in optimization theory and variational calculus

De Gruyter 2020, ISBN 9783110590852

Note:

Information about the course and teaching materials can be found at https://courses.fit.cvut.cz/QNI-OVV

Further information:

https://courses.fit.cvut.cz/QNI-OVV

No time-table has been prepared for this course

The course is a part of the following study plans:

• Quantum Informatics (compulsory elective course)