SF1811 Optimization 6.0 credits


Please note

The information on this page is based on a course syllabus that is not yet valid.

  • Education cycle

    First cycle
  • Main field of study

  • Grading scale

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

Course offerings

Autumn 19 for programme students

Autumn 18 for programme students

Autumn 18 Doktorand for single courses students

  • Periods

    Autumn 18 P2 (6.0 credits)

  • Application code


  • Start date


  • End date


  • Language of instruction


  • Campus

    KTH Campus

  • Tutoring time


  • Form of study


  • Number of places *

    Max. 1

    *) If there are more applicants than number of places selection will be made.

  • Course responsible

    Anders Szepessy <szepessy@kth.se>

  • Teacher

    Anders Szepessy <szepessy@kth.se>

  • Target group

    For doctoral student at KTH

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.

Course main content

  • 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.


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. 


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


  • TEN1 - Examination, 6.0, grading scale: A, B, C, D, E, FX, F

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.

Offered by



Anders Szepessy (szepessy@kth.se)


Anders Szepessy <szepessy@kth.se>

Supplementary information

SF1811 is today identical to SF1841, with common lectures and examination.

Add-on studies

SF2812 Applied Linear Optimization, SF2822 Applied Nonlinear Optimization


Course syllabus valid from: Autumn 2019.
Examination information valid from: Autumn 2007.