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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Offering and execution

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Course information

Content and learning outcomes

Course contents *

  • The simplex method and interior methods for linear programming.
  • Utilization of problem structure in linear programming, 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 large-scale integer programming problems with special structure.

Intended learning outcomes *

To pass the course, the student shall be able to:

  • Apply theory, concepts and methods from the parts of optimization that are given by the course contents to solve problems.
  • Model, formulate and analyze simplified practical problems as optimization problems and solve by making use of given software.
  • Collaborate with other students and demonstrate ability to present orally and in writing.

To receive the highest grade, the student should in addition be able to do the following:

  • Combine and explain the methods in the course, and
  • Apply and explain the theory and the concepts of the course in the practical problems that are included.

Course Disposition

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Literature and preparations

Specific prerequisites *

  • Completed basic course in optimization (SF1811, SF1861 or equivalent)
  • Completed basic course in mathematical statistics (SF1914, SF1918, SF1922 or equivalent)
  • Completed basic course in numerical analysis (SF1544, SF1545 or equivalent)
  • Completed basic course in differential equations (SF1633, SF1683 or equivalent).

Recommended prerequisites

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Equipment

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Literature

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.

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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Examiner

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

SCI/Mathematics

Main field of study *

Mathematics

Education cycle *

Second cycle

Add-on studies

No information inserted

Contact

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.