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Linear & Combinatorial Optimization
Last Updated: 2026-06-03 00:07:36
Abstract
Mathematical treatment of optimization techniques for linear and combinatorial optimization problems.
Objective
The goal of this course is to get a thorough understanding of various classical mathematical optimization techniques for linear and combinatorial optimization problems, with an emphasis on polyhedral approaches. In particular, we want students to develop a good understanding of some important problem classes in the field, of structural mathematical results linked to these problems, and of solution approaches based on such structural insights.
Content
Key topics include: - Linear programming and polyhedra; - Flows and cuts; - Combinatorial optimization problems and polyhedral techniques; - Equivalence between optimization and separation.
Resources
Literature
- Bernhard Korte, Jens Vygen: Combinatorial Optimization. 6th edition, Springer, 2018. - Alexander Schrijver: Combinatorial Optimization: Polyhedra and Efficiency. Springer, 2003. This work has 3 volumes. - Ravindra K. Ahuja, Thomas L. Magnanti, James B. Orlin. Network Flows: Theory, Algorithms, and Applications. Prentice Hall, 1993. - Alexander Schrijver: Theory of Linear and Integer Programming. John Wiley, 1986.
General Information
- Language
- English
- Levels
- BSC , MSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- written 180 minutes
- Aids
- None
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Linear & Combinatorial Optimization (Mathematical Optimization) | No time listed | 4 h weekly |
| exercise |
Linear & Combinatorial Optimization (Mathematical Optimization)
Thu 14-16 or Fri 10-12 or Fr 12-14 or Fri 14-16 (depending on demand)
|
No time listed | 2 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 (In the ‘electives’ subcategory, at least two course units must be successfully completed. All courses listed as core courses (not electives) for one of the following ETH MSc programmes, MSc Statistics, MSc Physics, MSc Computer Science, MSc (Applied) Mathematics, MSc Neural Systems and Computation, MSc Robotics, Systems, and Control, MSc Data Science, MSc Electrical Engineering and Information Technology, can be taken as an elective course in the MSc CSE without prior permission.)
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Core Courses (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 14 of the required 26 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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Electives (The entire course programs of ETH Zurich and Universitiy Zurich are open to the students to individual selection. The students have themselves to check whether they meet the admission requirements for a course.)
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Track: Systems and Control (The core courses and specialisation courses below are a selection for students who wish to specialise in the area of "Systems and Control", see . The individual study plan is subject to the tutor's approval.)
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Specialisation Courses (These specialisation courses are particularly recommended for the area of "Systems and Control", but you are free to choose courses from any other field in agreement with your tutor. Semester / Research Projects are not allowed in this category. A minimum of 40 credits must be obtained from specialisation courses during the Master's Programme.)
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Track: Signal Processing and Machine Learning (The core courses and specialisation courses below are a selection for students who wish to specialise in the area of "Signal Processing and Machine Learning ", see . The individual study plan is subject to the tutor's approval.)
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Specialisation Courses (These specialisation courses are particularly recommended for the area of "Signal Processing and Machine Learning", but you are free to choose courses from any other field in agreement with your tutor. A minimum of 40 credits must be obtained from specialisation courses during the MSc EEIT.)
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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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