Subjects

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Introduction to Mathematical Optimization - N413009

Title:	Základy matematické optimalizace
Guaranteed by:	Department of Mathematics (413)
Faculty:	Faculty of Chemical Engineering
Actual:	from 2019 to 2020
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:	20 / unknown (unknown)
Min. number of students:	unlimited
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Level:

Guarantor:	Turzík Daniel doc. RNDr. CSc.
Class:	Předměty pro matematiku
Is interchangeable with:	B413009, AB413009

Examination dates Schedule

Annotation -

The subject is designed for all students in bachelor programmes, especially aimed at economics. Students learn basic notions and algorithms in mathematical optimization.

Last update: TAJ413 (17.12.2013)

Aim of the course -

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: TAJ413 (05.09.2013)

Literature -

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

Last update: MAXOVAJ (20.01.2020)

Teaching methods -

Lectures and seminars

Last update: VED413 (04.09.2013)

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: VED413 (04.09.2013)

Learning resources -

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

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

Last update: MAXOVAJ (20.01.2020)

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