SF2812 Applied Linear Optimization 7.5 credits

Tillämpad linjär optimering

The course gives a deepened and broadened theoretical and methodological knowledge in linear and integer programming. Some subjects dealt with in the course are: The simplex methods, interior methods, decomposition, column generation, stochastic programming, Lagrangian relaxation and subgradient methods in integer programming.

The course also gives training in modeling and solving practical problems, and to present the results in talking as well as writing.

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Course information

Content and learning outcomes

Course contents *

Theory and methods:

The simplex method and interior point methods for linear programming. Utlization of problem structure, e.g., decomposition and column generation. Stochastic programming, methods and utilization of problem structure. Branch-and-bound methods for integer programming. Lagrangian relaxation and subgradient methods for integer programming problems with special structure.


This part of the course consists of modeling practical optimization problems and using available optimization software to solve them. The projects are carried out in small groups. An important aspect of the course is cooperation within the group as well as presentations in talking and in writing.

Intended learning outcomes *

To deepen and broaden the theoretical and methodological knowledge in linear and integer programming.

To give training in the art of modeling and solving practical problems, and in presenting the results in talking and in writing.

Course Disposition

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Literature and preparations

Specific prerequisites *

In general:

150 university credits (hp) including 28 hp in Mathematics,  6 hp in Mathematical Statistics and 6 hp in Optimization. Documented proficiency in English corresponding to English B.

More precisely for KTH students:

Passed courses in calculus, linear algebra, differential equations, mathematical statistics, numerical analysis, optimization.

Recommended prerequisites

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To be announced at the beginning of the course. Preliminary literature:

Linear and Nonlinear Programming by S.G.Nash och A.Sofer, McGraw-Hill, and some material from the department.

Examination and completion

Grading scale *

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

Examination *

  • PRO1 - Project, 1.5 credits, Grading scale: A, B, C, D, E, FX, F
  • PRO2 - Project, 1.5 credits, Grading scale: A, B, C, D, E, FX, F
  • TEN1 - Examination, 4.5 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.

Other requirements for final grade *

A written exam (TEN1; 4,5 hp).
Projects (PRO1; 3 hp).

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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Anders Forsgren

Further information

Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web SF2812

Offered by


Main field of study *


Education cycle *

Second cycle

Add-on studies

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Anders Forsgren (andersf@kth.se)

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.