SubjectsSubjects(version: 978)
Course, academic year 2019/2020
  
Introduction to Mathematical Optimization - B413009
Title: Základy matematické optimalizace
Guaranteed by: Department of Mathematics (413)
Faculty: Faculty of Chemical Engineering
Actual: from 2019 to 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 [HT]
Capacity: unknown / unknown (unknown)
Min. number of students: unlimited
Qualifications:  
State of the course: taught
Language: Czech
Teaching methods: full-time
Level:  
Note: course can be enrolled in outside the study plan
enabled for web enrollment
Guarantor: Turzík Daniel doc. RNDr. CSc.
Maxová Jana RNDr. Ph.D.
Classification: Mathematics > Optimization
Interchangeability : N413009
Examination dates   Schedule   
Annotation -
The course is intended for all students in bachelor programmes, particularly those studying chemical cybernetics or focusing on economics. Students will become familiar with fundamental concepts and methods used in optimization.
Last update: Szala Leszek Marcin (16.09.2025)
Literature -

Obligatory:

  • Boyd, Stephen and Vandenberghe, Lieven. Convex Optimization. Cambridge: Cambridge University Press, 2004, s. ISBN 978-0-521-83378-3.
  • Conforti, Michele and Cornuéjols, Gérard and Zambelli, Giacomo. Integer Programming. Cham: Springer, 2014, s. ISBN 978-3-319-11008-0.
  • Diestel, Reinhard. Graph theory. New York: Springer-Verlag, 2000, s. ISBN 978-3-662-53621-6.

Recommended:

  • Schrijver, A.. Theory of linear and integer programming. Chichester: Wiley, 1986, XI, 471 sl. s. ISBN 0-471-98232-6.

Optional:

  • Bertsimas, Dimitris and Tsitsiklis, John N.. Introduction to Linear Optimization. Belmont: Athena Scientific, 1997, s. ISBN 1-886529-19-1.

Last update: Szala Leszek Marcin (16.09.2025)
Teaching methods -

Lectures and seminars

Last update: Kubová Petra (01.05.2019)
Syllabus -

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.

Last update: MAXOVAJ (17.01.2020)
Learning resources -

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

Last update: Szala Leszek Marcin (16.09.2025)
Learning outcomes -

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 .

Last update: Kubová Petra (01.05.2019)
Registration requirements -

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

Last update: MAXOVAJ (20.01.2020)
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

 
VŠCHT Praha