Mathematical treatment of optimization techniques for linear and combinatorial optimization problems.
Learning 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.
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.
Prerequisites / Notice
Solid background in linear algebra.
Former course title: Mathematical Optimization.
Competencies
Subject-specific Competencies
Concepts and Theories
assessed
Techniques and Technologies
fostered
Method-specific Competencies
Analytical Competencies
assessed
Decision-making
assessed
Media and Digital Technologies
fostered
Problem-solving
assessed
Project Management
fostered
Social Competencies
Communication
assessed
Cooperation and Teamwork
fostered
Customer Orientation
fostered
Leadership and Responsibility
fostered
Self-presentation and Social Influence
fostered
Sensitivity to Diversity
fostered
Negotiation
fostered
Personal Competencies
Adaptability and Flexibility
fostered
Creative Thinking
assessed
Critical Thinking
fostered
Integrity and Work Ethics
fostered
Self-awareness and Self-reflection
fostered
Self-direction and Self-management
fostered
Performance assessment
Performance assessment information (valid until the course unit is held again)
The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examination
written 180 minutes
Additional information on mode of examination
There will be an optional graded interim exam in the second half of the semester. If the grade of the interim exam is better than the final one, then the interim exam contributes 30% to the final grade. If the grade of the interim exam is lower, or if the interim exam has not been taken, then the interim exam is ignored and the final grade for this course unit will be the grade of the final exam.
Credits can only be recognized for either "Mathematical Optimization" or for the previously offered course "Combinatorial Optimization" (401-4904-00L), but not both.
Written aids
None
This information can be updated until the beginning of the semester; information on the examination timetable is binding.