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Optimization, 6 credits

Optimeringslära, 6 hp

TNK049

Course starting semester

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Anders Peterson

Director of studies or equivalent

Erik Bergfeldt

Education components

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

Possible deviation from course syllabus/programme syllabus

ECV = Elective / Compulsory / Voluntary

Course offered for		Semester	Period	Timetable module	Language	Campus	ECV
6CKTS	Communications, Transport and Infrastructure, M Sc in Engineering	3 (Autumn 2017)	2	2	Swedish	Norrköping, Norrköping	C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G2X

Course offered for

Communications, Transport and Infrastructure, 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

Fundamentals in mathematical analysis and linear algebra

Intended learning outcomes

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.

Course content

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.

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, 5

Other information

Supplementary courses:
Advanced courses in optimization.

Department

Institutionen för teknik och naturvetenskap

Director of Studies or equivalent

Erik Bergfeldt

Examiner

Anders Peterson

Education components

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

Course literature

Additional literature

Books

Henningsson, M., Lundgren, J., Rönnqvist, M. och P. Värbrand, Optimeringslära: Övningsbok senaste
Lundgren, Jan, Rönnqvist, Mikael, Värbrand, Peter, (2008) Optimeringslära
ISBN: 9789144053141
Lund : Studentlitteratur, 2008

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.

Student rights and obligations (login required)
Linköping University common rules and regulations (in Swedish)

Additional literature

Books

Henningsson, M., Lundgren, J., Rönnqvist, M. och P. Värbrand, Optimeringslära: Övningsbok senaste

Lundgren, Jan, Rönnqvist, Mikael, Värbrand, Peter, (2008) Optimeringslära

ISBN: 9789144053141

Lund : Studentlitteratur, 2008

Download

Download course literature list as PDF

Note: The course matrix might contain more information in Swedish.

I = Introduce, U = Teach, A = Utilize

		I	U	A	Modules
1. DISCIPLINARY KNOWLEDGE AND REASONING
	1.1 Knowledge of underlying mathematics and science (G1X level)		X	X	LAB1 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	LAB1 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	LAB1 TEN1
	2.2 Experimentation, investigation, and knowledge discovery			X	LAB1
	2.3 System thinking	X	X	X	LAB1 TEN1
	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
	4.3 Conceiving, system engineering and management	X	X	X	LAB1 TEN1
	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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