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Course, academic year 2023/2024
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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 2020
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: not taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. RNDr. Martin Branda, Ph.D.
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 : NMFM204
Interchangeability : NMFM204
Is incompatible with: NMFM204, NMSA936
Is interchangeable with: NMFM204, NMAN007, NMSA936
In complex pre-requisite: NMSA349
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)
Course completion requirements -

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

Requirements for exercise class credit: The credit for the exercise class will be awarded to the student who is present at the exercise class sessions (two absences are tolerated) and hands in a satisfactory solution to each of five standard assignments to get 80% of total points and at the same time hands in a satisfactory solution to an additional homework on simplex algorithm.

The nature of these requirements precludes any possibility of additional attempts to obtain the exercise class credit.

It is probable that a large part of the exams could take place in a distance form. It depends on a development of the situation and we will inform you about the changes immediately.

Last update: Branda Martin, doc. RNDr., Ph.D. (28.04.2020)
Literature -

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. (in Czech only)

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

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

Last update: Branda Martin, doc. RNDr., Ph.D. (28.10.2019)
Teaching methods -

Lecture+exercises.

Last update: T_KPMS (15.05.2012)
Requirements to the exam -

The exam is in the form of written test, which consists of three computational examples (solved during practicals). The theory discussed during the lectures is part of the examples. It is necessary to get 60% of total points to pass.

It is probable that a large part of the exams could take place in a distance form. It depends on a development of the situation and we will inform you about the changes immediately.

Last update: Branda Martin, doc. RNDr., Ph.D. (28.04.2020)
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)
 
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