Discrete Optimization II (DiscOptII)10 ECTS
(englische Bezeichnung: Discrete Optimization II)

Lehrveranstaltungen:

• • Diskrete Optimierung II
    (Vorlesung, 4 SWS, Andreas Bärmann, Mi, 10:00 - 12:00, H12; Do, 10:00 - 12:00, Übung 4 / 01.253-128)
  • Übung Diskrete Optimierung II
    (Übung, 2 SWS, Andreas Bärmann et al.)

Empfohlene Voraussetzungen:

Knowledge in linear and combinatorial optimization, discrete optimization I

Inhalt:

In this lecture we cover theoretical aspects and solution strategies for difficult integer and mixed-integer optimization problems. First, we point out the equivalence between separation and optimization. Second, fundamental results of integral polyhedra, lattices and lattice polyhedra as well as its importance to discrete optimization are discussed. Furthermore, we introduce solution strategies for large-scale optimization problems, e.g., decomposition methods or approximation algorithms and heuristics based on linearprogramming. In addition, we discuss applications arising in engineering, finance, energymanagement or public transport.

Lernziele und Kompetenzen:

Students

• use basic terms of discrete optimization,

• model real-world discrete optimization problems, determine their complexity and solve them with appropriate mathematical methods.

Literatur:

• Lecture notes

• D. Bertsimas, R. Weismantel: Optimization over Integers, Dynamic Ideas, 2005

• Conforti, Cornuéjols, Zambelli: Integer Programming, Springer 2014

• G. L. Nemhauser, L.A. Wolsey: Integer and Combinatorial Optimization, Wiley 1994

• A. Schrijver: Combinatorial optimization Vol. A C, Springer 2003

• A. Schrijver: Theory of Linear and Integer Programming, Wiley, 1986 -L.A. Wolsey: Integer Programming, Wiley

Verwendbarkeit des Moduls / Einpassung in den Musterstudienplan:
Das Modul ist im Kontext der folgenden Studienfächer/Vertiefungsrichtungen verwendbar:

1. Computational and Applied Mathematics (Master of Science)
   (Po-Vers. 2017w | NatFak | Computational and Applied Mathematics (Master of Science) | Non-Specialisation modules | Discrete optimization II)
2. Computational and Applied Mathematics (Master of Science)
   (Po-Vers. 2017w | NatFak | Computational and Applied Mathematics (Master of Science) | Specialisation: Modeling and applied analysis (MApA) and optimization (Opti) | Discrete optimization II)
3. Computational and Applied Mathematics (Master of Science)
   (Po-Vers. 2017w | NatFak | Computational and Applied Mathematics (Master of Science) | Specialisation: Numerical analysis and simulation (NASi) and optimization (Opti) | Discrete optimization II)
4. 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 II)
5. 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 II)
6. Computational and Applied Mathematics (Master of Science)
   (Po-Vers. 2019w | NatFak | Computational and Applied Mathematics (Master of Science) | Gesamtkonto | Non-Specialisation modules | Discrete optimization II)
7. Informatik (Bachelor of Science)
   (Po-Vers. 2009s | TechFak | Informatik (Bachelor of Science) | Nebenfach | Nebenfach Mathematik | Discrete optimization II)
8. Informatik (Bachelor of Science)
   (Po-Vers. 2009w | TechFak | Informatik (Bachelor of Science) | Gesamtkonto | Nebenfach | Nebenfach Mathematik | Discrete optimization II)
9. Informatik (Master of Science)
   (Po-Vers. 2010 | TechFak | Informatik (Master of Science) | Gesamtkonto | Nebenfach | Nebenfach Mathematik | Discrete optimization II)
10. Wirtschaftsmathematik (Master of Science)
    (Po-Vers. 2019w | NatFak | Wirtschaftsmathematik (Master of Science) | Gesamtkonto | Mathematische Wahlpflichtmodule | Specialisation: Modeling and applied analysis (MApA) and optimization (Opti) | Discrete optimization II)
11. Wirtschaftsmathematik (Master of Science)
    (Po-Vers. 2019w | NatFak | Wirtschaftsmathematik (Master of Science) | Gesamtkonto | Mathematische Wahlpflichtmodule | Specialisation: Numerical analysis and simulation (NASi) and optimization (Opti) | Discrete optimization II)

Studien-/Prüfungsleistungen:

Discrete optimization II (Prüfungsnummer: 59221)

(englischer Titel: Discrete optimization II)

Prüfungsleistung, mündliche Prüfung, Dauer (in Minuten): 20, benotet, 10.0 ECTS

Anteil an der Berechnung der Modulnote: 100.0 %

Erstablegung: SS 2020, 1. Wdh.: SS 2020

1. Prüfer:

Andreas Bärmann