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 levelSecond cycle
Academic level (A-D)D
Grade scaleA, B, C, D, E, FX, F
PeriodsSpring 14 P3 (7.5 credits)
Start date2014 week: 4
End date2014 week: 12
Language of instructionEnglish
Number of lectures
Number of exercises
Form of studyNormal
Number of places *10 - 60
*) The Course date may be cancelled if number of admitted are less than minimum of places. If there are more applicants than number of places selection will be made.
ScheduleSchedule (new window)
Course responsibleAnders Forsgren <firstname.lastname@example.org>
TeacherAnders Forsgren <email@example.com>
Tove Odland <firstname.lastname@example.org>
Master students in Mathematics,
Master students in Applied and Computational Mathematics,
Master students in Aerospace Engineering,
Master students in Systems, Control and Robotics.
Part of programme
- Master (Two Years), Aerospace Engineering, year 1, SYS, Mandatory
- Master (Two Years), Applied and Computational Mathematics, year 1, Conditionally Elective
- Master (Two Years), Applied and Computational Mathematics, year 1, OPSA, Conditionally Elective
- Master (Two Years), Mathematics, year 1, Optional
- Master (Two Years), Mathematics, year 2, COMP, Optional
- Master (Two Years), Mathematics, year 2, OS, Recommended
- Master (Two Years), Systems, Control and Robotics, year 1, Recommended
- Master (Two Years), Systems, Control and Robotics, year 2, Recommended
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.
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.
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.
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.
- 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).
Course plan valid from:
Examination information valid from: Autumn 07.