M0160 Optimization Theory

Faculty of Science
Spring 2011
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)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 14:00–15:50 M6,01011
  • Timetable of Seminar Groups:
M0160/01: Tue 16:00–16:50 M6,01011, O. Došlý
Prerequisites
The course of Mathematical Programming is supposed for the part devoted to quadratic programming, generally knowledges from the course of Mathematical Analysis I-III are supposed.
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 Mathematical Programming (M5170) and presents optimization methods which are not treated in that course.
Syllabus
  • I. Quadratic programming in economic decision, methods of quadratic programming (continuation of the course Mathematical Programming M5171). II. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models - functional equation of dynamic programming. III. Elements of the calculus of variations: historical motivation, Euler-Lagrange equation and the first variation, second variation. Elements of optimal control theory, Pontryagin principle.
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
  • 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
  • LEWIS, Frank. Optimal Control. New York: John Wiley & Sons, 1986, 362 pp. A Wiley-Interscience Publication. ISBN 0-471-81240-4. info
Teaching methods
Theoretical lecture and excersise with illustrating examples
Assessment methods
The course is finished by an oral exam.
Language of instruction
Czech
Further comments (probably available only in Czech)
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 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 2024, Spring 2025.
  • Enrolment Statistics (Spring 2011, recent)
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