Course detail
Mathematical methods of project optimisation
FP-ImopKAcad. year: 2024/2025
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.
Guarantor
Department
Entry knowledge
Differential calculus of one and more variables, integral calculus, linear algebra, differential equations
Rules for evaluation and completion of the course
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.
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
" 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.
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
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.
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
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
Study aids
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.
Recommended reading
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-KS Master's 1 year of study, summer semester, compulsory-optional
Type of course unit
Guided consultation in combined form of studies
12 hod., 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.
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.