Course detail
Mathematical methods of project optimisation
FP-mopPAcad. year: 2022/2023
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
Number of ECTS credits
Mode of study
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Department
Learning outcomes of the course unit
Prerequisites
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
" 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
Aims
Specification of controlled education, way of implementation and compensation for absences
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Prerequisites and corequisites
Basic literature
Recommended reading
Classification of course in study plans
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
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.