Introduction to Optimization, 6 credits

Optimeringslära grundkurs, 6 hp

TAOP07

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Torbjörn Larsson

Director of studies or equivalent

Ingegerd Skoglund

Education components

Preliminary scheduled hours: 60 h
Recommended self-study hours: 100 h
ECV = Elective / Compulsory / Voluntary
Course offered for Semester Period Timetable module Language Campus ECV
6CMED 8 (Spring 2017) 1 3 Swedish Linköping E
6CMED (Biomedical Imaging and Visualization) 8 (Spring 2017) 1 3 Swedish Linköping E
6CMED (Biomedical Modelling) 8 (Spring 2017) 1 3 Swedish Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 4 (Spring 2017) 1 3 Swedish Linköping C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 4 (Spring 2017) 1 3 Swedish Linköping C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 4 (Spring 2017) 1 3 Swedish Linköping C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 4 (Spring 2017) 1 3 Swedish Linköping C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 4 (Spring 2017) 1 3 Swedish Linköping C
6CYYY Applied Physics and Electrical Engineering, M Sc in Engineering 4 (Spring 2017) 1 3 Swedish Linköping C
6CMJU Computer Science and Software Engineering, M Sc in Engineering 8 (Spring 2017) 1 3 Swedish Linköping C/E
6MDAV Computer Science, Master's programme 2 (Spring 2017) 1 3 Swedish Linköping E
6KMAT Mathematics 4 (Spring 2017) 1 3 Swedish Linköping C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G1X

Course offered for

  • Applied Physics and Electrical Engineering - International, M Sc in Engineering
  • Applied Physics and Electrical Engineering, M Sc in Engineering
  • Mathematics
  • Computer Science, Master's programme
  • Computer Science and Software 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

Calculus, linear algebra, and Matlab

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 a broad orientation of the field of optimization, with emphasis on basic theory and methods for continuous and discrete optimization problems in finite dimension, and it also gives some insight into its use for analyzing practical optimization problems. After the course, the student shall be able to:

  • identify optimization problems and classify them according to their properties, into, for example, linear and nonlinear, or continuous and discrete, problems
  • construct mathematical models of simple optimization problems
  • define and use basic concepts, such as, for example, local and global optimality, convexity, weak and strong duality, and valid inequalities
  • reproduce and apply basic theory for some common types of optimization problems, such as, for example, duality theory for linear optimization problems, and have knowledge about and be able to use optimality conditions, such as, for example, Bellman's equations, to determine the optimality of a given solution
  • describe and apply basic principles for solving some common types of optimization problems, such as, for example, branch-and-bound for discrete problems
  • use relaxations, and especially Lagrangian duality, to approximate optimization problems, and be able to estimate the optimal objective value through lower and upper bounds
  • use commonly available software for solving optimization problems of standard type.

Course content

Fundamental concepts within optimization, such as mathematical modelling, optimality conditions, convexity, sensitivity analysis, duality, and Lagrangean relaxation. Basic theory and methods for linear and nonlinear optimization, and integer and network optimization.

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

TEN1Written examination5 creditsU, 3, 4, 5
LAB1Laboratory Work1 creditsU, G

Grades

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

Other information

Supplementary courses: Optimization, advanced course Y, Applied optimization - project course, Mathematical optimization.

Department

Matematiska institutionen

Director of Studies or equivalent

Ingegerd Skoglund

Examiner

Torbjörn Larsson

Course website and other links

http://courses.mai.liu.se/GU/TAOP07

Education components

Preliminary scheduled hours: 60 h
Recommended self-study hours: 100 h

Course literature

Jan Lundgren, Mikael Rönnqvist och Peter Värbrand: Optimeringslära (Studentlitteratur). Exempelsamling: Optimeringslära grk för Y.
Code Name Scope Grading scale
TEN1 Written examination 5 credits U, 3, 4, 5
LAB1 Laboratory Work 1 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. 

Jan Lundgren, Mikael Rönnqvist och Peter Värbrand: Optimeringslära (Studentlitteratur). Exempelsamling: Optimeringslära grk för Y.

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

                            
1.2 Fundamental engineering knowledge (G1X level)
X

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

                            
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

                            
2.2 Experimentation, investigation, and knowledge discovery

                            
2.3 System thinking
X

                            
2.4 Attitudes, thought, and learning
X

                            
2.5 Ethics, equity, and other responsibilities

                            
3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
3.1 Teamwork
X

                            
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

                            
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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