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Geometric Integer Programming
Last Updated: 2026-02-05 15:41:56
Abstract
Integer programming is the task of minimizing a linear function over all the integer points in a polyhedron. This lecture introduces the key concepts of an algorithmic theory for solving such problems.
Objective
The purpose of the lecture is to provide a geometric treatment of the theory of integer optimization.
Content
Key topics are: - Lattice theory and the polynomial time solvability of integer optimization problems in fixed dimension. - Structural properties of integer sets that reveal other parameters affecting the complexity of integer problems - Duality theory for integer optimization problems from the vantage point of lattice free sets.
Resources
Lecture Notes
not available, blackboard presentation
Literature
Lecture notes will be provided. Other helpful materials include Bertsimas, Weismantel: Optimization over Integers, 2005 and Schrijver: Theory of linear and integer programming, 1986.
Learning Materials (Links)
- Additional links
- Information on other courses offered at IFOR
General Information
- Language
- English
- Levels
- DR , MSC
Examination
- Type
- session examination
- Mode
- oral 30 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Geometric Integer Programming |
|
2 h weekly |
| exercise | Geometric Integer Programming |
|
1 h weekly |
Offered In
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Electives (In the ‘electives’ subcategory, at least two course units must be successfully completed.)
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Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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Statistics Master (The following courses belong to the curriculum of the Master's Programme in Statistics. The corresponding credits do not count as external credits even for course units where an enrolment at ETH Zurich is not possible.)
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Doctoral Department of Mathematics (More Information at: The list of courses (together with the allocated credit points) eligible for doctoral students is published each semester in the newsletter of the ZGSM. WARNING: Do not mistake ECTS credits for credit points for doctoral studies!)
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Graduate School (Official website of the Zurich Graduate School in Mathematics:)
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