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SF1811 Optimization 6.0 credits

SF1811 is a basic course on optimization.

Choose semester and course offering

Choose semester and course offering to see current information and more about the course, such as course syllabus, study period, and application information.


For course offering

Autumn 2024 Start 28 Oct 2024 programme students

Application code


Headings with content from the Course syllabus SF1811 (Autumn 2019–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

  • Examples of applications of optimization and modelling training.
  • Basic concepts and theory for optimization, in particular theory for convex problems.
  • Linear algebra in Rn, in particular bases for the four fundamental subspaces corresponding to a given matrix, and LDLT-factorization of a symmetric positive semidefinite matrix.
  • Linear optimization, including duality theory.
  • Optimization of flows in networks.
  • Quadratic optimization with linear equality constraints.
  • Linear least squares problems, in particular minimum norm solutions.
  • Unconstrained nonlinear optimization, in particular nonlinear least squares problems.
  • Optimality conditions for constrained nonlinear optimization, in particular for convex problems.
  • Lagrangian relaxation.

Intended learning outcomes

After completing the course students should for a passing grade be able to

  • Apply basic theory, concepts and methods, within the parts of optimization theory described by the course content, to solve problems
  • Formulate simplified application problems as optimization problems and solve using software.
  • Read and understand mathematical texts about for example,  linear algebra, calculus and optimization and their applications, communicate mathematical reasoning and calculations in this area, orally and in writing in such a way that they are easy to follow.

For higher grades the student should also be able to

  • Explain, combine and analyze basic theory, concepts and methods within the parts of optimization theory described by the course content.

Literature and preparations

Specific prerequisites

Completed  course in SF1624 Linear algebra and geometry or SF1672 Linear Algebra.
Completed course in SF1626 Calculus in several variables or SF1674 Multivariable Calculus.
Completed course in Numerical analysis, SF1511, SF1519, SF1545 or  SF1546. 

Recommended prerequisites

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The literature is published on the course webpage no later than four weeks before the course starts.

Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

Grading scale

A, B, C, D, E, FX, F


  • INL1 - Home assignment, 2.0 credits, grading scale: P, F
  • TEN2 - Exam, 4.0 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

The examiner decides, in consultation with KTHs Coordinator of students with disabilities (Funka), about any customized examination for students with documented,lastingdisability. The examiner may allow another form of examination for reexamination of individual students.

Opportunity to complete the requirements via supplementary examination

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Opportunity to raise an approved grade via renewed examination

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Ethical approach

  • All members of a group are responsible for the group's work.
  • In any assessment, every student shall honestly disclose any help received and sources used.
  • In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further information

Course room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

Offered by

Main field of study

Mathematics, Technology

Education cycle

First cycle

Add-on studies

SF2812 Applied Linear Optimization, SF2822 Applied Nonlinear Optimization


Anders Forsgren (