M0160 Optimization Theory

Faculty of Science
Spring 2013
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
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 8:00–9:50 M4,01024
  • Timetable of Seminar Groups:
M0160/01: Fri 10:00–10:50 M4,01024, 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 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
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. 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
Teaching methods
Theoretical lecture
Assessment methods
The course is finished by an oral exam. The student usually gets two questions. The knowledge of basic concepts of both two questions is needed to pass. What does it mean ``knowledge of the basic cenceps'' depends of a particular quastion which is a student given.
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 2011, Spring 2012, spring 2012 - acreditation, 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 2013, recent)
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