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Large Scale Optimization, 6 credits
Optimering av stora system, 6 hp
TAOP34
Main field of study
Mathematics Applied MathematicsCourse level
Second cycleCourse type
Programme courseExaminer
Torbjörn LarssonDirector of studies or equivalent
Ingegerd SkoglundEducation components
Preliminary scheduled hours: 64 hRecommended self-study hours: 96 h
Available for exchange students
YesECV = Elective / Compulsory / Voluntary
Main field of study
Mathematics, Applied MathematicsCourse level
Second cycleAdvancement level
A1XCourse offered for
- Mathematics, Master's Programme
- Industrial Engineering and Management - International, M Sc in Engineering
- Industrial Engineering and Management, M Sc in Engineering
- Applied Physics and Electrical Engineering - International, M Sc in Engineering
- Applied Physics and Electrical Engineering, M Sc in Engineering
- Mechanical Engineering, 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
An introductory course in optimization.Intended learning outcomes
The course aims at giving insight into the practical application of optimization methodology to technical and economic decision problems, and to give knowledge about solution principles for certain classes of structured large-scale optimization problems that frequently arise in practical applications. After the course, the student shall:
- be able to state and describe the mathematical principles that are used to decompose optimization problems
- be able to apply decomposition methods to solve structured optimization problems
- be acquainted with applications of decomposition methods, be able to identify applications that are well suited for such methods, and be able to choose a suitable methodology and use thereof
- have an enhanced knowledge of the practical use of optimization methodology.
Course content
Advanced linear programming and column generation. Price-directive decentralized planning and the Dantzig-Wolfe decomposition principle. Lagrangean relaxation and subgradient optimization. Application to problems arising in for example facility location and in the planning of production and distribution.
Teaching and working methods
The lectures cover model building, theory, and solution methods for large-scale optimization, and give examples of applications. The participants in the course present solutions to assignments, which include numerical excercises, theoretical questions, and further applications. The laboratory exercises comprise the solution of specially structured optimization problems using standard computer software.
Examination
| MUN1 | Examination | 6 credits | U, 3, 4, 5 |
| UPG1 | Exercise | 0 credits | U, G |
Grades
Four-grade scale, LiU, U, 3, 4, 5Other information
Supplementary courses:
Supply chain optimization.
Department
Matematiska institutionenDirector of Studies or equivalent
Ingegerd SkoglundExaminer
Torbjörn LarssonCourse website and other links
http://courses.mai.liu.se/GU/TAOP34Education components
Preliminary scheduled hours: 64 hRecommended self-study hours: 96 h
Course literature
Utdelat material.| Code | Name | Scope | Grading scale |
|---|---|---|---|
| MUN1 | Examination | 6 credits | U, 3, 4, 5 |
| UPG1 | Exercise | 0 credits | U, G |
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.
Utdelat material.
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
|
MUN1
|
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| 1.2 Fundamental engineering knowledge (G1X level) |
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| 1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level) |
|
X
|
|
MUN1
|
||
| 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
|
X
|
MUN1
|
||
| 2.2 Experimentation, investigation, and knowledge discovery |
|
|
X
|
UPG1
|
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| 2.3 System thinking |
|
X
|
X
|
MUN1
|
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| 2.4 Attitudes, thought, and learning |
|
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X
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MUN1
|
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| 2.5 Ethics, equity, and other responsibilities |
|
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| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
|
|
X
|
UPG1
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| 3.2 Communications |
|
|
X
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MUN1
|
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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 |
|
X
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MUN1
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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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