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Blekinge Institute of Technology
Department of Mathematics and Natural Science

Revision: 2
Reg.no: BTH-4.1.14-0034-2025


Course syllabus

Optimization

Optimization

6 credits (6 högskolepoäng)

Course code: MA1502
Main field of study: Mathematics
Disciplinary domain: Natural sciences
Education level: First-cycle
Specialization: G1F - First cycle, has less than 60 credits in first-cycle course/s as entry requirements

Language of instruction: English
Applies from: 2025-02-18
Approved: 2025-02-18

1. Descision

This course is established by Dean 2023-02-03. The course syllabus is approved by Head of Department of Mathematics and Natural Science 2025-02-18 and applies from 2025-02-18.

2. Entry requirements

Admission to the course requires taken course in Multivariable Calculus, 5 credits, and 5 completed credits in Linear Algebra. English 6.

3. Objective and content

3.1 Objective

The course aims to provide knowledge in various linear programming problems, to find solutions to linear programs, and to show applications of linear optimization theory to various theoretical and practical subjects.

3.2 Content

· Examples of linear programming
· Graphic representation and reading
· The geometry of linear programming
· Simplex method
· Duality theory
· Primal and dual problem formulations
· Optimization with multiple variables and constraints
· Nonlinear and nonlinear convex optimization problems
· Karush-Kuhn-Tucker conditions
· Lagrange functions 
· Combinatorial optimization

4. Learning outcomes

The following learning outcomes are examined in the course:

4.1. Knowledge and understanding

On completion of the course, the student will be able to:

  • demonstrate an understanding of basic principles and geometry for optimization.
  • know what linear optimization and especially linear programming is and how it works.
  • know what a nonlinear program is.
  • formulate the Lagrange function and determine the dual Lagrange function for convex optimization problems.
  • know the most common English terms in the field of optimization.
  • understand the meaning of primal and dual problem formulations.

4.2. Competence and skills

On completion of the course, the student will be able to:

  • use Lagrange's multiplier theorem.
  • solve simpler linear problems with the complementarity theorem.
  • solve linear and nonlinear convex optimization problems based on the Karush-Kuhn-Tucker theorem.
  • verify with the Karush-Kuhn-Tucker conditions that a solution to a nonlinear convex optimization problem is optimal.
  • translate problem formulations into programs.

4.3. Judgement and approach

On completion of the course, the student will be able to:

  • independently analyze and propose solution principles for different types of optimization problems.

5. Learning activities

The course is given as a campus course with lectures, laboratory session and exercises.

6. Assessment and grading

Modes of examinations of the course

Code Module Credit Grade
2510 Written examination[1] 3.5 credits AF
2520 Laboratory session 2.5 credits GU

[1] Determines the final grade for the course, which will only be issued when all components have been approved.

The course will be graded A Excellent, B Very good, C Good, D Satisfactory, E Sufficient, FX Failed result, a little more work required, F Fail.

The examiner may carry out oral follow-up of written examinations.

The information before the start of the course states the assessment criteria and make explicit in which modes of examination that the learning outcomes are assessed.

An examiner can, after consulting the Disability Advisor at BTH, decide on a customized examination form for a student with a long-term disability to be provided with an examination equivalent to one given to a student who is not disabled.

7. Course evaluation

The course evaluation should be carried out in line with BTH:s course evaluation template and process.

8. Restrictions regarding degree

The course can form part of a degree but not together with another course the content of which completely or partly corresponds with the contents of this course.

9. Course literature and other materials of instruction

Lundgren, J. et al. (2010) Optimization. First edition. Studentlitteratur. ISBN: 9789144053080.

Materials distributed by the department may be added.

This is not a legal document. If you would like a copy of the legal decision regarding this course plan, contact the registrar at Blekinge Institute of Technology.