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Optimization, 6 credits
Optimization, 6 hp
TNK053
Main field of study
Mathematics Applied MathematicsCourse level
First cycleCourse type
Programme courseExaminer
Zhuangwei LiuDirector of studies or equivalent
George BaravdishEducation components
Preliminary scheduled hours: 48 hRecommended self-study hours: 112 h
Available for exchange students
YesECV = Elective / Compulsory / Voluntary
| Course offered for | Semester | Period | Timetable module | Language | Campus | ECV | |
|---|---|---|---|---|---|---|---|
| 6MTSL | Intelligent Transport Systems and Logistics, Master's Programme | 1 (Autumn 2017) | 2 | 1 | English | Norrköping, Norrköping | C |
Main field of study
Mathematics, Applied MathematicsCourse level
First cycleAdvancement level
G2XCourse offered for
- Intelligent Transport Systems and Logistics, Master's Programme
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
Linear Algebra and Multivariable CalculusIntended learning outcomes
The course will provide basic insight in optimization, especially optimization of linear, nonlinear, and integer problems and problems with a network structure. The students can, after completing the course, formulate and analyze optimization models in the area of economic and technical applications; comprehend the basic mathematical theory on which the model and algorithms are based on; and be able to solve optimization problem both manually and with the help of a computer.
Course content
Linear programming: Modelling, basic mathematical theory and geometry, the simplex method, sensitivity analysis, duality, optimality conditions.
Nonlinear optimization: Modelling, convexity, unconstrained optimization, optimization under constraints, optimality conditions.
Network optimization: Modelling, shortest paths.
Integer optimization: Modelling, cutting plane and branch and bound.
Teaching and working methods
Lectures, exercises and laborations
Examination
| LAB1 | Laboratory work | 1.5 credits | U, G |
| TEN1 | Written examination | 4.5 credits | U, 3, 4, 5 |
Grades
Four-grade scale, LiU, U, 3, 4, 5Department
Institutionen för teknik och naturvetenskapDirector of Studies or equivalent
George BaravdishExaminer
Zhuangwei LiuCourse website and other links
http://www2.itn.liu.se/utbildning/kurs/index.html?coursecode=TNK053Education components
Preliminary scheduled hours: 48 hRecommended self-study hours: 112 h
Course literature
Additional literature
Books
- Winston, Wayne L., Venkataramanan, Munirpallam, Goldberg, Jeffrey B., (2003) Introduction to mathematical programming : operations research
ISBN: 0534359647, 9780534359645
Pacific Grove, CA : Thomson/Brooks/Cole Duxbury, c2003.
| Code | Name | Scope | Grading scale |
|---|---|---|---|
| LAB1 | Laboratory work | 1.5 credits | U, G |
| TEN1 | Written examination | 4.5 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.
Additional literature
Books
Winston, Wayne L., Venkataramanan, Munirpallam, Goldberg, Jeffrey B., (2003) Introduction to mathematical programming : operations research
ISBN: 0534359647, 9780534359645
Pacific Grove, CA : Thomson/Brooks/Cole Duxbury, c2003.
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) |
|
X
|
X
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TEN1
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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
|
X
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X
|
TEN1
|
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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
|
X
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X
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TEN1
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| 2.2 Experimentation, investigation, and knowledge discovery |
|
X
|
X
|
LAB1
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| 2.3 System thinking |
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| 2.4 Attitudes, thought, and learning |
X
|
X
|
X
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TEN1
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| 2.5 Ethics, equity, and other responsibilities |
X
|
X
|
X
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LAB1
TEN1
|
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| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
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X
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LAB1
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| 3.2 Communications |
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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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X
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TEN1
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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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