SubjectsSubjects(version: 845)
Course, academic year 2018/2019
   Login via CAS
Optimisation Theory - NMSA403
Title in English: Teorie optimalizace
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018 to 2019
Semester: winter
E-Credits: 5
Hours per week, examination: winter s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: doc. RNDr. Petr Lachout, CSc.
Class: M Mgr. FPM
M Mgr. FPM > Povinně volitelné
M Mgr. PMSE
M Mgr. PMSE > Povinné
Classification: Mathematics > Optimization
Is pre-requisite for: NMEK436, NMEK532, NMEK450
Annotation -
Last update: RNDr. Jitka Zichová, Dr. (02.05.2018)
Optimization in economy and statistics, convex analysis, introduction to non-linear programming, theory of linear programming with respect to convex analysis and general optimization. Supposed knowledge: Mathematical analysis (functions with several arguments, constraint extrema problems).
Aim of the course -
Last update: T_KPMS (14.05.2013)

To give explanation and theoretical background for standard optimization procedures. Students will lern necessary theory and practice their knowladge on numerical examples.

Course completion requirements -
Last update: doc. RNDr. Petr Lachout, CSc. (11.10.2017)

The course is finalized by a credit from the exercises class and exam.

The exercises class credit is necessary to sign up for the exam.

Conditions for receiving of a credit from exercises class are:

  • At least 70% actively attended exercises.
  • Successful passing the test at the end of the semester (it is necessary to get at least 70% points).

Attempt to receive a credit from exercises class cannot be repeated.

Literature - Czech
Last update: T_KPMS (20.04.2015)

Bazaraa, M.S.; Sherali, H.D.; Shetty, C.M.: Nonlinear programming: theory and algorithms. Wiley, New York, 1993.

Bertsekas, D.P.: Nonlinear programming. Athena Scientific, Belmont, 1999.

Dantzig, G.B.; Thapa, M.N.: Linear programming. 1,2. Springer, New York, 1997.

Luenberger, D.G.; Ye, Y.: Linear and Nonlinear Programming. 3rd edition, Springer, New York, 2008.

Plesník, J.; Dupačová, J.; Vlach, M.: Lineárne programovanie. Alfa, Bratislava, 1990.

Rockafellar, T.: Convex Analysis. Springer-Verlag, Berlin, 1975.

Rockafellar, T.; Wets, R. J.-B.: Variational Analysis. Springer-Verlag, Berlin, 1998.

Teaching methods -
Last update: T_KPMS (14.05.2013)

Lecture + exercises.

Requirements to the exam -
Last update: doc. RNDr. Petr Lachout, CSc. (11.10.2017)

The exam is contained from written part and oral part. Written part is foregoing to oral part.

If written part is not fulfilled, whole exam is marked as non-satisfactory, and oral part is not treated.

Mark from the examination is determined considering results from both written and oral part.

If student did not pass the exam, he must repeat both written part and oral part next time.

Examination is checking knowledge of all matters read by the class lecturer.

The exercises class credit is necessary to sign up for the exam.

Conditions for receiving of a credit from exercises class are:

  • At least 70% actively attended exercises.
  • Successful passing the test at the end of the semester (it is necessary to get at least 70% points).

Attempt to receive a credit from exercises class cannot be repeated.

Syllabus -
Last update: doc. RNDr. Petr Lachout, CSc. (27.04.2018)

1. Optimization problems and their formulations.

2. Selected parts of convex analyses (convex cones, convex function, epigraph, subdifferential).

3. Separation theorems (Farkas theorem).

4. Theory of nonlinear programming. (Karush-Kuhn-Tucker optimality condition, constraints qualifications).

5. Linear a convex programming like a particular case of nonlinear programming.

6. Symmetric problem of nonlinear programming.

Entry requirements -
Last update: doc. RNDr. Petr Lachout, CSc. (30.05.2018)

introduction to optimization theory, convex analysis, functional analysis

 
Charles University | Information system of Charles University | http://www.cuni.cz/UKEN-329.html