SubjectsSubjects(version: 945)
Course, academic year 2014/2015
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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 2014 to 2014
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
Teaching methods: full-time
Guarantor: 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 incompatible with: NMSA936
Is interchangeable with: NMAN007, NMSA936
In complex pre-requisite: NMSA349
Annotation -
Last update: G_M (16.05.2012)
Introduction to optimization theory. Recommended for bachelor's program in General Mathematics, specialization Stochastics.
Aim of the course -
Last update: T_KPMS (25.04.2016)

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.

Literature - Czech
Last update: T_KPMS (25.04.2016)

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.

Teaching methods -
Last update: T_KPMS (15.05.2012)

Lecture+exercises.

Syllabus -
Last update: T_KPMS (25.04.2016)

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.

 
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