M5170 Mathematical Programming

Faculty of Science
Autumn 2009
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
prof. RNDr. Roman Šimon Hilscher, DSc. (alternate examiner)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 12:00–13:50 M1,01017
  • Timetable of Seminar Groups:
M5170/01: Thu 14:00–14:50 M1,01017, O. Došlý
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 aim of the course is to provide the basic fact of the convex and its application to optimization problems in finitedimensonal spaces. A particular attention is devoted to the convex programming and to some numerical methods of optimization.
Syllabus
  • I. Convex analysis. Convex sets: basic concepts, convex hull, separation and supporting hyperplanes. Convex Functions: basic concepts, convexity criteria for differentiable functions, subgradient and subdifferential, Fenchel transformation, system of linear and convex inequalities. II. Duality, necessary and sufficient conditions for optimality. Lagrange principle, Kuhn-Tucker conditions, casic concepts of convex progamming. Duality in mathematical programming, dual problem, Kuhn-Tucker vrctor, saddle point. Duality in special optimization problems {linear and quadratic}. III. Numerical methods of minimization. Onedimensional minimization {Fibonaci and golden ratio methods} Unconstrained optimization (steepest slope method, method of conjugate gradients, Newton method}. Quadratic programming {Wolfe method and modofications, Thiel van de Panne method}.
Literature
  • DOŠLÝ, Ondřej. Základy konvexní analýzy a optimalizace v Rn. 1. vyd. Brno: Masarykova univerzita, 2005, viii, 185. ISBN 8021039051. info
  • HAMALA, Milan. Nelineárne programovanie. 2., dopl. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1976, 240 s. info
Teaching methods
Theoretical lecture and seminar
Assessment methods
The standard lecture and accompany exercise, the exam has written and oral part.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2009, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2009/M5170