The aim of studying and bibliography

The main aim of study: Preparing students to use algorithms and non-linear programming techniques to solve optimization problems

The general information about the module: The module is implemented in the fifth semester (15 hours of lectures, 15 hours of laboratory classes and 15 hours of project classes)

Bibliography required to complete the module

Bibliography used during lectures

1	J.G. Ecker, M. Kupferschmid	Introduction to Operations Research	John Wiley & Sons, New York.	1988
2	W. Findeisen, J. Szymanowski, A. Wierzbicki	Teoria i metody obliczeniowe optymalizacji	PWN, Warszawa.	1980

Bibliography used during classes/laboratories/others

1	H. Wickham	Język R: kompletny zestaw narzędzi dla analityków danych	Wydawnictwo Helion, Gliwice .	2018
2	P. Biecek	Przewodnik po pakiecie R	GiS, Wrocław .	2017

Bibliography to self-study

1

K. Kukuła (red.)

Badania operacyjne w przykładach i zadaniach

PWN, Warszawa.

2016

Basic requirements in category knowledge/skills/social competences

Formal requirements: The fifth semester of a degree in engineering and data analysis. The student satisfies the formal requirements set out in the study regulations.

Basic requirements in category knowledge: Knowledge of basic concepts of linear algebra and mathematical analysis

Basic requirements in category skills: Ability to perform operations on matrices and vectors, solving systems of linear equations, calculating derivatives and integrals. Knowledge of the basics of programming in R

Basic requirements in category social competences: Willingness to continue to acquire mathematical knowledge. Ability to work in a group

Module outcomes

MEK	The student who completed the module	Types of classes / teaching methods leading to achieving a given outcome of teaching	Methods of verifying every mentioned outcome of teaching	Relationships with KEK	Relationships with PRK
01	understands the basic concepts of non-linear programming, knows optimality conditions and can determine the minimum and maximum of a function of one and many variables (without constraints)	lectures, laboratory and project classes	written test, project evaluation	K_W02+ K_W03++ K_U03++ K_U24+ K_K02+	P6S_KK P6S_KO P6S_UK P6S_UO P6S_UW P6S_WG
02	knows how to use the Lagrange multipliers method and how to identify inactive constraints, knows the selected properties of convex functions and the basics of the Karush-Kun-Tucker theory	lectures, laboratory and project classes	written test, project evaluation	K_W02+ K_W03++ K_U03++ K_U24+ K_K02+	P6S_KK P6S_KO P6S_UK P6S_UO P6S_UW P6S_WG
03	knows selected numerical methods of nonlinear optimization and can apply them in simple situations using the R Program	laboratory and project classes	project evaluation	K_W02+ K_U03+++ K_U08+ K_U25+ K_K04++	P6S_KO P6S_KR P6S_UU P6S_UW P6S_WG

Attention: Depending on the epidemic situation, verification of the achieved learning outcomes specified in the study program, in particular credits and examinations at the end of specific classes, can be implemented remotely (real-time meetings).

The syllabus of the module

Sem.	TK	The content	realized in	MEK
5	TK01	Optimization of functions of one variable - selected numerical methods	W1-W2, L1-L4	MEK01 MEK03
5	TK02	Unconstrained non-linear optimization problem: problem formulation, optimality conditions, minimization and maximization of functions of several variables	W3-W8, L5-L8	MEK01 MEK03
5	TK03	Problem of nonlinear optimization with constraints: equality constraints - the Lagrange method, inactive constraints - the condition of orthogonality, convex functions and their selected properties, elements of the Karush-Kun-Tucker theory	W9-W15, L9-L15	MEK02 MEK03
5	TK04	The R Programm and its application to modeling and solving selected nonlinear optimization problems	L1-L15, P1-P10	MEK01 MEK02 MEK03
5	TK05	Project presentation	P11-P15	MEK03

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 5)		contact hours: 15.00 hours/sem.
Laboratory (sem. 5)		contact hours: 15.00 hours/sem.	Finishing/Making the report: 4.00 hours/sem.
Project/Seminar (sem. 5)	The preparation for projects/seminars: 3.00 hours/sem.	contact hours: 15.00 hours/sem..	Doing the project/report/ Keeping records: 5.00 hours/sem. The preparation for the presentation: 1.00 hours/sem. Others: 1.00 hours/sem.
Advice (sem. 5)		The participation in Advice: 1.00 hours/sem.
Credit (sem. 5)

The way of giving the component module grades and the final grade

The type of classes	The way of giving the final grade
Lecture	Pass of the lecture is based on a positive assessment of all projects
Laboratory	Pass of the laboratory is based on a positive assessment of all projects
Project/Seminar	Pass of the project classes is based on a positive assessment of all projects
The final grade	The final grade is the arithmetic mean of the grades for individual projects.

Sample problems

Required during the exam/when receiving the credit
(-)

Realized during classes/laboratories/projects
OL.pdf

Others
(-)

Can a student use any teaching aids during the exam/when receiving the credit : no

The contents of the module are associated with the research profile: no