M0160 Optimization

Faculty of Science
Spring 2024
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Petr Zemánek, Ph.D. (lecturer)
Guaranteed by
doc. Mgr. Petr Zemánek, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 19. 2. to Sun 26. 5. Tue 10:00–11:50 M1,01017
  • Timetable of Seminar Groups:
M0160/01: Mon 19. 2. to Sun 26. 5. Fri 12:00–13:50 M1,01017, P. Zemánek
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
After this course the studnets get knowledge and skill concerning basic methods of solutions of some optimization problems.
Learning outcomes
At the end of this course the students will be able to solve problems of the linear, integer, quadratic, and dynamic programming as well as basic problems of calculus of variations.
Syllabus
  • I. Linear programming.
  • Ia. Integer programming.
  • II. Quadratic programming.
  • III. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models.
  • IV. Elements of the calculus of variations and discrete optimization: historical motivation, Euler-Lagrange equation and the first variation, second variation, elementary difference equations and recurrence relations, discrete calculus of variations.
Literature
    recommended literature
  • DOŠLÝ, Ondřej. Základy konvexní analýzy a optimalizace v R^n (Elements of convex analysis and optimization in R^n). 1st ed. Brno: Masarykova univerzita, 2005, 194 pp. ISBN 80-210-3905-1. info
  • DANTZIG, George Bernard and Mukund Narain THAPA. Linear programming. New York: Springer, 2003, xxv, 448 s. ISBN 0-387-98613-8. info
  • BAZARAA, Mokhtar S., John J. JARVIS and Hanif D. SHERALI. Linear programming and network flows. 2nd ed. New York: John Wiley & Sons, Inc., 1990, xiv+684 pp. ISBN 0-471-63681-9. info
  • KÜNZI, Hans P., Wilhelm KRELLE and Werner OETTLI. Nichtlineare Programmierung. Berlin: Springer-Verlag, 1962, 221 s. info
  • HAMALA, Milan. Nelineárne programovanie. 2. dopl. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1972, 240 s. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
  • BELLMAN, Richard. Dynamic programming. Dover ed. Mineola, N.Y.: Dover Publications, 2003, xxv, 340. ISBN 0486428095. info
  • GEL'FAND, Izrail Moisejevič and Sergej Vasil'jevič FOMIN. Calculus of variations. Edited by Richard A. Silverman. Mineola, N. Y.: Dover Publications, 2000, vii, 232 s. ISBN 0-486-41448-5. info
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
Teaching methods
Lectures and exercises.
Assessment methods
The exam has both written and oral components. In the written part students solve particular examples. In the oral part a question concerning one of the topic I-IV (see the syllabus above) is given and the knowledge of basic concepts is required.

The conditions (especially regarding the form of the tests and exam) will be specified according to the epidemiological situation and valid restrictions.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents. The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics. Assessment in all cases may be in Czech and English, at the student's choice.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2025.
  • Enrolment Statistics (recent)
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