Subjects

Your browser does not support JavaScript, or its support is disabled. Some features may not be available.

Optimisation Theory - NMSA403

Title:	Teorie optimalizace
Guaranteed by:	Department of Probability and Mathematical Statistics (32-KPMS)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2016 to 2017
Semester:	winter
E-Credits:	5
Hours per week, examination:	winter s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech, English
Teaching methods:	full-time
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
Incompatibility :	NEKN012
Interchangeability :	NEKN012
Is pre-requisite for:	NMEK436, NMEK450, NMEK532
Is interchangeable with:	NEKN012, NEKN035

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: RNDr. Jitka Zichová, Dr. (02.05.2018)

Optimization in economy and statistics, introduction to non-linear programming, theory of linear programming with respect to convex analysis and general optimization, overview of available optimization software, matrix games. The contents of the course and seminar is organized so that the lecture could be attended without the seminar.

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.

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.

Syllabus -

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

1. Optimisation problems and their formulations. Application in statistics a economy.

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

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

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

5. Introduction in nonsmooth optimisation (tangent and normal cone, Clark constraints qualification).

6. Introduction in game theory (games of two players with zero sum, minimax theorem).