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Optimization, Advanced Course, 6 credits
Optimeringslära fortsättningskurs, 6 hp
TAOP24
Main field of study
Mathematics Applied MathematicsCourse level
First cycleCourse type
Programme courseExaminer
Oleg BurdakovDirector of studies or equivalent
Ingegerd SkoglundEducation components
Preliminary scheduled hours: 38 hRecommended self-study hours: 122 h
Available for exchange students
YesECV = Elective / Compulsory / Voluntary
Main field of study
Mathematics, Applied MathematicsCourse level
First cycleAdvancement level
G2XCourse offered for
- Mathematics
- Applied Physics and Electrical Engineering, M Sc in Engineering
- Computer Science, Master's programme
- Applied Physics and Electrical Engineering - International, M Sc in Engineering
Entry requirements
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.
Prerequisites
Introduction to optimization.Intended learning outcomes
Optimization deals with mathematical theory and methods aiming at analyzing and solving decision problems that arise in technology, economy, medicine, etc. The course gives, together with the introductory course, a broad orientation of the field of optimization. After the course, the student shall:
- be able to identify optimization problems and classify them according to their properties, into, for example, network problems or discrete problems
- construct mathematical models of more complex optimization problems
- have knowledge about and be able to apply basic solution principles for some classes of commonly appearing optimization problems, such as, for example, the simplex method for network flows
- be able to use commonly available software for solving optimization problems that appear regularly in applications
- be able to use relaxations to approximate optimization problems and heuristic methods for finding feasible solutions, and be able to estimate the optimal objective value through lower and upper bounds
- have good knowledge about practical applications of optimization
methodologies
Course content
A continuation of the material presented in the introductory course. The course includes more advanced topics within mathematical modelling, network optimization, sensitivity analysis in linear programming, discrete optimization, nonlinear optimization, and Lagrangian relaxation. Some new topics are also included, such as dynamic programming and heuristics.
Teaching and working methods
Lectures which include theory, problem solving and applications. Exercises which are intended to give individual training in problem solving. A laboratory course with emphasis on modelling and the use of optimization software.
Examination
LAB1 Laboratory course 2 credits U, G TEN1 Written examination 4 credits U, 3, 4, 5 Grades
Four-grade scale, LiU, U, 3, 4, 5Other information
Supplementary courses: Mathematical optimization.
Department
Matematiska institutionenDirector of Studies or equivalent
Ingegerd SkoglundExaminer
Oleg BurdakovCourse website and other links
http://courses.mai.liu.se/GU/TAOP24Education components
Preliminary scheduled hours: 38 h
Recommended self-study hours: 122 hCourse literature
Jan Lundgren, Mikael Rönnqvist & Peter Värbrand - Optimeringslära (Studentlitteratur, 2008). Jan Lundgren, Mathias Henningsson & Mikael Rönnqvist -Optimeringslära övningsbok (Studentlitteratur, 2008)
| Code | Name | Scope | Grading scale |
|---|---|---|---|
| LAB1 | Laboratory course | 2 credits | U, G |
| TEN1 | Written examination | 4 credits | U, 3, 4, 5 |
Regulations (apply to LiU in its entirety)
The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.
LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva.
Course literature is preliminary.
Jan Lundgren, Mikael Rönnqvist & Peter Värbrand - Optimeringslära (Studentlitteratur, 2008). Jan Lundgren, Mathias Henningsson & Mikael Rönnqvist -Optimeringslära övningsbok (Studentlitteratur, 2008)
Note: The course matrix might contain more information in Swedish.
I = Introduce, U = Teach, A = Utilize
| I | U | A | Modules | Comment | ||
|---|---|---|---|---|---|---|
| 1. DISCIPLINARY KNOWLEDGE AND REASONING | ||||||
| 1.1 Knowledge of underlying mathematics and science (G1X level) |
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X
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X
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| 1.2 Fundamental engineering knowledge (G1X level) |
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X
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| 1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level) |
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| 1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level) |
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| 1.5 Insight into current research and development work |
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| 2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES | ||||||
| 2.1 Analytical reasoning and problem solving |
X
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X
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X
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| 2.2 Experimentation, investigation, and knowledge discovery |
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| 2.3 System thinking |
X
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| 2.4 Attitudes, thought, and learning |
X
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| 2.5 Ethics, equity, and other responsibilities |
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| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
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X
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| 3.2 Communications |
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X
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| 3.3 Communication in foreign languages |
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| 4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT | ||||||
| 4.1 External, societal, and environmental context |
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| 4.2 Enterprise and business context |
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| 4.3 Conceiving, system engineering and management |
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X
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| 4.4 Designing |
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| 4.5 Implementing |
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| 4.6 Operating |
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| 5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS | ||||||
| 5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development |
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| 5.2 Economic conditions for knowledge development |
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| 5.3 Identification of needs, structuring and planning of research or development projects |
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| 5.4 Execution of research or development projects |
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| 5.5 Presentation and evaluation of research or development projects |
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