Course detail

Mathematical Methods in Logistics

FSI-SMA-AAcad. year: 2024/2025

The subject is focused on selected optimization tasks. Attention will be paid in particular to the tasks of convex optimization, calculus of variations and the basics of optimal control.

Language of instruction

English

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. Mgr. Petr Vašík, Ph.D.

Department

Institute of Mathematics (ÚM)

Entry knowledge

Knowledge of foundations of the following topics is required:

  • differential and integral calculus of one-variable functions
  • vector and matrix calculus
  • numerical optimisation
  • probability

Rules for evaluation and completion of the course

Credit will be awarded for the semester assessment. This will be a specific task on a selected topic that shoud be processed individually. The exam will take the form of a project defense, which will be assigned no later than the 10th week of the semester.


Aims

Not applicable.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

W. Forst and D. Hoffmann,  Optimization―Theory and Practice, Springer Undergraduate Texts in Mathematics and Technology, 2010th Edition, [2010]. (EN)
M. Athans and P. L. Falb, Optimal control: an introduction to the theory and its applications. Mineola: Dover Publications, [2007].  (EN)
M. H. Veatch, Linear and Convex Optimization: A Mathematical Approach, Wiley, [2021]. (EN)

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme N-LAN-A Master's, 1. year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

doc. Mgr. Petr Vašík, Ph.D.

Syllabus

Week 1-3: Introduction to convex optimisation, convex functions, convex sets
Week 4-5: Quadratic programming
Week 6-9: Numerical optimisation methods, Newton's method, gradient descent method and conjugate gradient method
Week 10-13: Variational methods, introduction to optimal control of dynamical systems

Exercise

26 hours, compulsory

Teacher / Lecturer

doc. Mgr. Petr Vašík, Ph.D.

Syllabus

In the first exercise we recall elementary notions from analytical geometry and numerical methods. Tutorial examples will be calculated. Further exercises will topically follow the lectures from the previous week.