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Introduction to Optimisation - NMSA336

Title:	Úvod do optimalizace
Guaranteed by:	Department of Probability and Mathematical Statistics (32-KPMS)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2012 to 2013
Semester:	summer
E-Credits:	4
Hours per week, examination:	summer s.:2/1, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time

Guarantor:	doc. RNDr. Petr Lachout, CSc.
Teacher(s):	Mgr. Lukáš Adam, Ph.D. RNDr. Václav Kozmík, Ph.D. doc. RNDr. Petr Lachout, CSc.
Class:	M Bc. FM M Bc. FM > Povinné M Bc. FM > 2. ročník M Bc. OM M Bc. OM > Povinně volitelné M Bc. OM > Zaměření STOCH
Classification:	Mathematics > Optimization
Pre-requisite :	{One course in Linear Algebra}, {One 1st year course in Analysis or Calculus}
Incompatibility :	NEKN012, NMAN007
Interchangeability :	NEKN012, NMAN007
Is interchangeable with:	NMAN007
In complex pre-requisite:	NMSA349

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Annotation -

Introduction to optimization theory. Recommended for bachelor's program in General Mathematics, specialization Stochastics.

Last update: G_M (16.05.2012)

Aim of the course -

The goal is to give explanation and theoretical background for standard optimization procedures. Students will learn necessary theory and practice their knowledge on numerical examples.

Last update: T_KPMS (25.04.2016)

Literature - Czech

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.

Dupačová, J., Lachout, P.: Úvod do optimalizace. MatfyzPress, Praha, 2011.

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

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

Wolsey, L.A.: Integer Programming, Wiley, New York, 1998.

Last update: T_KPMS (25.04.2016)

Teaching methods -

Lecture+exercises.

Last update: T_KPMS (15.05.2012)

Syllabus -

1. Optimization problems and their formulations. Applications in economics, finance, logistics and mathematical statistics.

2. Basic parts of convex analysis (convex sets, convex multivariate functions).

3. Linear Programming (structure of the set of feasible solutions, simplex algorithm, duality, Farkas theorem).

4. Integer Linear Programming (applications, branch-and-bound algorithm).

5. Nonlinear Programming (local and global optimality conditions, constraint qualifications).

6. Quadratic Programming as a particular case of nonlinear programming problem.

Last update: T_KPMS (25.04.2016)