M0160 Optimization Theory

Faculty of Science
Spring 2015
Extent and Intensity
2/1. 2 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
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 11:00–12:50 M2,01021
  • Timetable of Seminar Groups:
M0160/01: Fri 13:00–13:50 M2,01021, P. Zemánek
Prerequisites
The course of M5170 Mathematical Programming is suitable for the part devoted to the linear and quadratic programming. Generally, knowledges from the course of Mathematical Analysis I-III are suitable.
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
The course is a free continuation of the course M5170 Mathematical Programming and presents optimization methods which are not treated in that course. At the of this course the students will be able to solve problems of the linear, quadratic, and dynamic programming as well as basic problems of calculus of variations.
Syllabus
  • I. Linear programming.
  • II. Quadratic programming.
  • III. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models - functional equation of dynamic programming.
  • 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
  • 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
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. 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
Theoretical lecture with illustrative examples.
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.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
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 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (Spring 2015, recent)
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