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Discrete Optimization (DiscOpt I)5 ECTS (englische Bezeichnung: Discrete Optimization)
(Prüfungsordnungsmodul: Discrete optimization I)
Modulverantwortliche/r: Alexander Martin Lehrende:
Andreas Bärmann
Start semester: |
WS 2019/2020 | Duration: |
1 semester | Cycle: |
unregelmäßig |
Präsenzzeit: |
45 Std. | Eigenstudium: |
105 Std. | Language: |
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Lectures:
Empfohlene Voraussetzungen:
Recommended: Linear and Combinatorial Optimization
Inhalt:
Theoretical and practical fundamentals of solving difficult mixed-integer linear
optimization problems (MIPs) constitute the main focus of this lecture. At first, the
concept of NP-completeness and a selection of common NP-complete problems will be
presented. As for polyhedral theory, fundamentals concerning the structure of faces of
convex polyhedra will be covered. Building upon these fundamentals, cutting plane
algorithms as well as branch-and-cut algorithms for solving MIPs will be taught. Finally,
some typical problems of discrete optimization, e.g., the knapsack problem, the
traveling salesman problem or the set packing problem will be discussed.
Lernziele und Kompetenzen:
Students
optimization problems (MIPs),
Literatur:
- Lecture notes
Conforti, Cornuéjols, Zambelli: Integer Programming, Springer 2014
B. Grünbaum, Convex Polytopes, Springer, 2003
B. Korte, J. Vygen: Combinatorial Optimization, Springer 2005
G. L. Nemhauser, L.A. Wolsey: Integer and Combinatorial Optimization, Wiley
1994
A. Schrijver: Theory of Linear and Integer Programming, Wiley 1986
L.A. Wolsey: Integer Programming, Wiley 1998
G. Ziegler, Lectures on Polytopes, Springer, 1995
Verwendbarkeit des Moduls / Einpassung in den Musterstudienplan:
- Computational and Applied Mathematics (Master of Science)
(Po-Vers. 2019w | NatFak | Computational and Applied Mathematics (Master of Science) | Gesamtkonto | Specialisation: Modeling and applied analysis (MApA) and optimization (Opti) | Discrete optimization I)
- Computational and Applied Mathematics (Master of Science)
(Po-Vers. 2019w | NatFak | Computational and Applied Mathematics (Master of Science) | Gesamtkonto | Specialisation: Numerical analysis and simulation (NASi) and optimization (Opti) | Discrete optimization I)
- Computational and Applied Mathematics (Master of Science)
(Po-Vers. 2019w | NatFak | Computational and Applied Mathematics (Master of Science) | Gesamtkonto | Non-Specialisation modules | Discrete optimization I)
Dieses Modul ist daneben auch in den Studienfächern "Informatik (Bachelor of Science)", "Informatik (Master of Science)" verwendbar. Details
Studien-/Prüfungsleistungen:
Discrete optimization I (Prüfungsnummer: 59171)
(englischer Titel: Discrete optimization I)
- Prüfungsleistung, mündliche Prüfung, Dauer (in Minuten): 15, benotet, 5 ECTS
- Anteil an der Berechnung der Modulnote: 100.0 %
- Erstablegung: WS 2019/2020, 1. Wdh.: WS 2019/2020
1. Prüfer: | Andreas Bärmann |
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