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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.

  • Educational level

    Second cycle

  • Academic level (A-D)

    D

  • Subject area

    Mathematics

  • Grade scale

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

Course offerings

Spring 14 for programme students

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 main content

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.

Projects:

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.

Eligibility

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.

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

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

Requirements for final grade

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

Offered by

SCI/Mathematics

Examiner

Anders Forsgren

Version

Course plan valid from: Autumn 11.
Examination information valid from: Autumn 07.