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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Content and learning outcomes
- 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.
Literature and preparations
- 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).
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
If the course is discontinued, students may request to be examined during the following two academic years.
- 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
The examiner may apply another examination format when re-examining individual students.
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed examination
- 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.
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