Introduction to Mathematical Optimization - N413009
Title: Základy matematické optimalizace
Guaranteed by: Department of Mathematics (413)
Actual: from 2019
Semester: summer
Points: summer s.:5
E-Credits: summer s.:5
Examination process: summer s.:
Hours per week, examination: summer s.:2/2 C+Ex [hours/week]
Capacity: unknown / unknown (unknown)
Min. number of students: unlimited
Language: Czech
Teaching methods: full-time
Level:  
For type:  
Note: course can be enrolled in outside the study plan
enabled for web enrollment
Guarantor: Turzík Daniel doc. RNDr. CSc.
Class: Předměty pro matematiku
Z//Is interchangeable with: B413009, AB413009
Examination dates   
Annotation -
Last update: TAJ413 (17.12.2013)
The subject is designed for all students in bachelor programmes, especially aimed at economics. Students learn basic notions and algorithms in mathematical optimization.
Aim of the course -
Last update: TAJ413 (05.09.2013)

General skills:

1. basic terms in mathematical optimiztion

2. knowledge and understanding of basic algorithms

3. individual problem solving

4. basic mathematical background for formulation and solving of optimization problems

5. numerical algorithms .

Literature -
Last update: Maxová Jana RNDr. Ph.D. (20.01.2020)

A: Dimitris Bertsimas and John N. Tsitsiklis : Introduction to Linear Optimization, 1997, ISBN-10: 1-886529-19-1

A: Alexander Schrijver : Theory of Linear and Integer Programming, New York 1986, ISBN-10: 0471982326

Learning resources -
Last update: Maxová Jana RNDr. Ph.D. (20.01.2020)

http://www.vscht.cz/mat/ZMO/Optim_maple.html

https://iti.mff.cuni.cz/series/2006/311.pdf

Teaching methods -
Last update: VED413 (04.09.2013)

Lectures and seminars

Syllabus -
Last update: VED413 (04.09.2013)

1. Problems of mathematical optimization.

2. Linear programming.

3. Convex polyhedra.

4. Simplex method.

5. Duality of linear programming.

6. Integer programming, totally unimodular matrices.

7. Basic notions of graph theory.

8. Shortest path problem.

9. Tree, spanning tree, greedy algorithm.

10. Discrete optimalization problems as problems of integer programming.

11. Nonlinear optimization.

12. Kuhn-Tucker conditions.

13. Numerical methods for nonlinear programming.

14. Convex functions, positive semidefinite matrices.

Registration requirements -
Last update: Maxová Jana RNDr. Ph.D. (20.01.2020)

Mathematics A, Mathematics B (or Mathematics I, Mathematics II)

Teaching methods
Activity Credits Hours
Účast na přednáškách 1 28
Příprava na přednášky, semináře, laboratoře, exkurzi nebo praxi 0,5 14
Práce na individuálním projektu 1 28
Příprava na zkoušku a její absolvování 1,5 42
Účast na seminářích 1 28
5 / 5 140 / 140
Coursework assessment
Form Significance
Regular attendance 20
Report from individual projects 30
Examination test 30
Oral examination 20