| TNK049 |
Optimization, 6 ECTS credits.
/Optimeringslära/
For:
KTS
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Prel. scheduled
hours: 48
Rec. self-study hours: 112
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Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
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Advancement level
(G1, G2, A): G2
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Aim:
The course provides basic insights in optimization, especially optimization of linear and nonlinear (continuous) problems and problems with a network structure. After completing the course, the student should be able to:
analyze and formulate linear optimization models in the areas of economical and technical applications.
analyze and formulate optimization models for problems with an underlying network structure.
comprehend the basic mathematical theory on which the models and algorithms are based.
apply and utilize optimization methods for optimization problems in continuous variable, such as the simplex method, the simplex method adapted for network problems, descent methods for unconstrained problems and the Frank–Wolfe algorithm.
analyze optimization models with respect to convexity and formulate optimality conditions for problems in continuous variables.
solve optimization problem both manually and by using computer software.
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Fundamentals in mathematical analysis and linear algebra
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
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Supplementary courses:
Advanced courses in optimization.
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Organisation:
Lectures, exercises and laborations.
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Course contents:
- Linear programming: Modeling, basic mathematical theory and geometry, the simplex method, sensitivity analysis, duality, optimality conditions.
- Nonlinear optimization: Modeling, convexity, unconstrained optimization, linearly constrained optimization, optimality conditions.
- Network optimization: Modeling, tree problems, path problems, versions of the minimum cost flow problem and the simplex method applied to problems with network structure.
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Course literature:
Lundgren, J., Rönnqvist, M. and P. Värbrand, Optimeringslära, Studentlitteratur, latest edition.
Henningsson, M., Lundgren, J., Rönnqvist, M. and P. Värbrand, Optimeringslära: Övningsbok, Studentlitteratur, latest edition.
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Examination: |
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Written examination
Laboratory work
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4,5 ECTS
1,5 ECTS
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Course language is Swedish.
Department offering the course: ITN.
Director of Studies: Erik Bergfeldt
Examiner: Anders Peterson
Link to the course homepage at the department
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