Course detail

# Mathematical methods of project optimisation

Completion and deepening of mathematical knowledge to students continuing in the master study of more immediate practical need areas - optimization problems, matrix games and linear programming, nonlinear programming, and more.

Language of instruction

Czech

Number of ECTS credits

4

Mode of study

Not applicable.

Learning outcomes of the course unit

The student will be able to analyze a problem primarily, to clarify the appropriate way to address and assess the accuracy of the solution with respect to specified conditions

Prerequisites

Differential calculus of one and more variables, integral calculus, linear algebra, differential equations

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Instructing is divided into lectures and exercises. Lectures are focused on the theory referring to applications, exercises on practical calculations and solving of application tasks.

Assesment methods and criteria linked to learning outcomes

Requirements to obtain a closure :
" to attend exercise sessions according to the given conditions of controlled classes

The exam is composed of two parts- written and oral, whereby a written part makes the main proportion.
The length of a written part is 1 hour. Written part is evaluated as the sum of ratings of both tasks. If a student does not obtain at least 50% points out of all, the written part and the whole exam is graded "F" and a student does not proceed to oral part.

Course curriculum

1. Optimization problems and their formulation. Applications in statistics and economics.
2. Fundamentals of Convex Analysis (convex sets, convex functions of several variables).
3. The role of linear programming (duality, structure of the set of admissible solutions, simplex method, Farkas theorem). Transportation problem as a special type of linear programming.
4. Additional to the linear programming (post-optimalization, stability). Matrix games and linear programming, Minimax theorem.
5. The symmetrical nonlinear programming (local and global optimality conditions, conditions of regularity).
6. Quadratic programming as a special type of symmetric nonlinear programming.

Work placements

Not applicable.

Aims

The aim is to complement and deepen knowledge of mathematics students in the master's continuing study of more immediate practical need in the game.

Specification of controlled education, way of implementation and compensation for absences

Attendance at lectures is not controlled. Attendance at exercises(problem sessions) is compulsory and is regularly checked. A student is obliged to give reasons for his absence. The teacher has a full competency to judge the reasons. In the affirmative, the teacher states the form of the compensation for the missed classes

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

DUPAČOVÁ, J., LACHOUT, P . Úvod do optimalizace. Vyd. 1. Praha: Matfyzpress, 2011, 81 s. ISBN 978-80-7378-176-7.

ŠTECHA, Jan. Optimální rozhodování a řízení. Praha: Vydavatelství ČVUT, 2002. 241 s. ISBN 80-01-02083-5.

Classification of course in study plans

• Programme MGR-IM Master's, 2. year of study, summer semester, compulsory-optional

• Programme MGR-SI Master's

branch MGR-IM , 2. year of study, summer semester, compulsory-optional

#### Type of course unit

Lecture

10 hours, optionally

Teacher / Lecturer

Syllabus

1. Optimization problems and their formulation. Applications in statistics and economics.
2. Fundamentals of Convex Analysis (convex sets, convex functions of several variables).
3. The role of linear programming (duality, structure of the set of admissible solutions, simplex method, Farkas theorem). Transportation problem as a special type of linear programming.
4. Additional to the linear programming (post-optimalization, stability). Matrix games and linear programming, Minimax theorem.
5. The symmetrical nonlinear programming (local and global optimality conditions, conditions of regularity).
6. Quadratic programming as a special type of symmetric nonlinear programming.

Exercise

10 hours, compulsory

Teacher / Lecturer