Mathematical Methods in Logistics (FSI-SMA-A)

Academic year 2024/2025
Supervisor: doc. Mgr. Petr Vašík, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: English
Aims of the course unit:
 
Learning outcomes and competences:
 
Prerequisites:

Knowledge of foundations of the following topics is required:

  • differential and integral calculus of one-variable functions
  • vector and matrix calculus
  • numerical optimisation
  • probability
Course contents:
 
Teaching methods and criteria:
 
Assesment methods and criteria linked to learning outcomes:
 
Controlled participation in lessons:
 
Type of course unit:
    Lecture  13 × 2 hrs. optionally                  
    Exercise  13 × 2 hrs. compulsory                  
Course curriculum:
    Lecture

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

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.
Literature - fundamental:
1. W. Forst and D. Hoffmann,  Optimization―Theory and Practice, Springer Undergraduate Texts in Mathematics and Technology, 2010th Edition, [2010].
2. M. Athans and P. L. Falb, Optimal control: an introduction to the theory and its applications. Mineola: Dover Publications, [2007]. 
3. M. H. Veatch, Linear and Convex Optimization: A Mathematical Approach, Wiley, [2021].
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
N-LAN-A full-time study --- no specialisation -- Cr,Ex 5 Compulsory 2 1 S