Optimization, 6 credits

Optimization, 6 hp

TNK053

The course is disused. Offered for the last time Autumn semester 2022. Replaced by TNK127.

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Zhuangwei Liu

Director of studies or equivalent

George Baravdish

Education components

Preliminary scheduled hours: 48 h
Recommended self-study hours: 112 h

Available for exchange students

Yes
ECV = 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 C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G2X

Course 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 Calculus

Intended 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

LAB1Laboratory work1.5 creditsU, G
TEN1Written examination4.5 creditsU, 3, 4, 5

Grades

Four-grade scale, LiU, U, 3, 4, 5

Department

Institutionen för teknik och naturvetenskap

Director of Studies or equivalent

George Baravdish

Examiner

Zhuangwei Liu

Course website and other links

http://www2.itn.liu.se/utbildning/kurs/index.html?coursecode=TNK053

Education components

Preliminary scheduled hours: 48 h
Recommended 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
TEN1

                            
1.2 Fundamental engineering knowledge (G1X level)

                            
1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level)
X
X
X
TEN1

                            
1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level)

                            
1.5 Insight into current research and development work

                            
2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES
2.1 Analytical reasoning and problem solving
X
X
X
TEN1

                            
2.2 Experimentation, investigation, and knowledge discovery
X
X
LAB1

                            
2.3 System thinking

                            
2.4 Attitudes, thought, and learning
X
X
X
TEN1

                            
2.5 Ethics, equity, and other responsibilities
X
X
X
LAB1
TEN1

                            
3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
3.1 Teamwork
X
LAB1

                            
3.2 Communications

                            
3.3 Communication in foreign languages

                            
4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT
4.1 External, societal, and environmental context

                            
4.2 Enterprise and business context
X
TEN1

                            
4.3 Conceiving, system engineering and management
X

                            
4.4 Designing

                            
4.5 Implementing

                            
4.6 Operating

                            
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

                            
5.2 Economic conditions for knowledge development

                            
5.3 Identification of needs, structuring and planning of research or development projects

                            
5.4 Execution of research or development projects

                            
5.5 Presentation and evaluation of research or development projects

                            

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