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Mathematical Optimization, 6 credits
Matematisk optimering, 6 hp
TAOP04
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: 36 hRecommended self-study hours: 124 h
ECV = 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
- Information Technology, M Sc in Engineering
- Applied Physics and Electrical Engineering - International, M Sc in Engineering
- Applied Physics and Electrical Engineering, M Sc in Engineering
- Mathematics, Master's programme
Specific information
The course is offered every second year. It will not be available during 2017
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, Matlab, and an introductory course in optimization.Intended learning outcomes
The course intends to give a deeper knowledge of mathematical optimization, with emphasis on solution methods for nonlinear optimization. After the course, the student shall be able to:
- reproduce and apply basic convergence theory for nonlinear optimization
- describe and apply some basic solution principles for nonlinear optimization, such as, for example, conjugate gradient methods
- understand the structure and function of commonly used computer software for nonlinear optimization.
Course content
Algorithmic mappings, line-search methods, the simplex method for unconstrained optimization, conjugate gradient methods, quasi-Newton methods, sequential linear programming, sequential quadratic programming, model predictive control (MPC), Gauss-Newton methods.
Teaching and working methods
The lectures develop the theory.
Examination
| UPG1 | Project | 6 credits | U, 3, 4, 5 |
Grades
Four-grade scale, LiU, U, 3, 4, 5Department
Matematiska institutionenDirector of Studies or equivalent
Ingegerd SkoglundExaminer
Torbjörn LarssonCourse website and other links
Education components
Preliminary scheduled hours: 36 hRecommended self-study hours: 124 h
Course literature
Additional literature
Compendia
Handouts
| Code | Name | Scope | Grading scale |
|---|---|---|---|
| UPG1 | Project | 6 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
Compendia
Handouts
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
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UPG1
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| 1.2 Fundamental engineering knowledge (G1X level) |
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X
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UPG1
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| 1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level) |
|
X
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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
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X
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UPG1
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| 2.2 Experimentation, investigation, and knowledge discovery |
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X
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UPG1
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| 2.3 System thinking |
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X
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UPG1
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| 2.4 Attitudes, thought, and learning |
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X
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UPG1
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| 2.5 Ethics, equity, and other responsibilities |
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| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
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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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| 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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