Diskrete Mathematik II - Optimierung W21/22
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Description

Attention: For the time being the tutorial will be held online and not at FU. Please follow the link below to access the Webex session,

Optimization 1 Tutorial Session
Hosted by Ricardo Euler

https://fu-berlin.webex.com/fu-berlin-en/j.php?MTID=m9a8e8814562709f96d842e0e4c707fbe
Friday, Dec 3, 2021 4:15 pm | 1 hour 30 minutes | (UTC+01:00) Amsterdam, Berlin, Bern, Rome, Stockholm, Vienna
Occurs every Friday effective 12/3/2021 until 2/11/2022 from 4:15 PM to 5:45 PM, (UTC+01:00) Amsterdam, Berlin, Bern, Rome, Stockholm, Vienna
Meeting number: 2734 932 5642
Password: Y6h3WJpBEq2

Join by video system
Dial 27349325642@fu-berlin.webex.com
You can also dial 62.109.219.4 and enter your meeting number.

Join by phone
+49-619-6781-9736 Germany Toll
+49-89-95467578 Germany Toll 2
Access code: 273 493 25642

 

 

 

The first tutorial will be held this Friday, 22.10.21 at 4:30 p.m. to accommodate students that want to go to the exam review session for Discrete Maths I at 4 p.m.

Please check out the Info Sheet. It contains all relevant information about the format of the lectures, tutorials and exercises.

Diese Vorlesung startet den Optimierungszweig der Diskreten Mathematik. Sie behandelt die Algorithmische Graphentheorie und die Lineare Optimierung.

Inhalt

  1. Komplexität: Komplexitätsmaße, Laufzeit von Algorithmen, die Klassen P und NP, NP-Vollständigkeit
  2. Matroide und Unabhängigkeitssysteme: Unabhängigkeitssysteme, Matroide, Bäume, Wälder, Orakel, Optimierung über Unabhängigkeitssystemen
  3. Kürzeste Wege: Nichtnegative Gewichte, allgemeine Gewichte, all pairs
  4. Netzwerflüsse: Das Max-Flow-Min-Cut Theorem, Augmentierende Wege, Minimalkostenflüsse, Transport- und Zuordnungsprobleme
  5. Polyeder: Seitenflächen, Dimensionsformel, Projektionen von Polyedern, Transformation, Polarität, Darstellungssätze.
  6. Grundlagen der Linearen Optimierung: Farkas Lemma, Dualitätssatz.
  7. Simplexalgorithmus: Basis, Degeneration, Basistausch, revidierter Simplexalgorithmus, Schranken, dualer Simplexalgorithmus, Postoptimierung, Numerik.
  8. Innere Punkte und Ellipsoidmethode: Grundlagen

Zielgruppe

Diese Veranstaltung richtet sich an Studierende der Mathematik mit Vorkenntnissen in Diskreter Mathematik, Linearer Algebra und Analysis. Einige Übungsaufgaben erfordern den Einsatz eines Computers.

 

Literatur

 

M. Grötschel, Lineare Optimierung, eines der Vorlesungsskripte

V. Chvátal, Linear Programming, Freeman 1983

Additional 

Garey&Johnson, Computers and Intractability,  1979 (Complexity Theory)

Bertsimas&Tsitsiklis, Introduction to Linear Optimization, 97 (Linear Programming)

Korte&Vygen, Combinatorial Optimization, 2006 (Flows, Shortest Paths, Matchings)

 

 

 

Zusätzliche Informationen

 

Anrechnung

Diese Veranstaltung kann als Diskrete Mathematik II (DM II) gewählt werden.

Bei gleichzeitiger Belegung von Diskrete Mathematik II - Extremale Kombinatorik kann einer der beiden Kurse als DM II und der andere als Ergänzungsmodul gewählt werden.

Sprache

Die VL findet auf Englisch statt.

Basic Course Info

Course No Course Type Hours
19234401 Vorlesung 4
19234402 Übung 2

Time Span 19.10.2021 - 01.03.2022
Instructors
Ralf Borndörfer
Ricardo Euler
Felix Maximilian Merz

Study Regulation

0089c_MA120 2014, MSc Informatik (Mono), 120 LPs
0280b_MA120 2011, MSc Mathematik (Mono), 120 LPs
0280c_MA120 2018, MSc Mathematik (Mono), 120 LP

Diskrete Mathematik II - Optimierung W21/22
to Whiteboard Site

Main Events

Day Time Location Details
Tuesday 12-14 A6/SR 007/008 Seminarraum 2021-10-19 - 2022-02-15
Wednesday 12-14 A6/SR 007/008 Seminarraum 2021-10-20 - 2022-02-16

Accompanying Events

Day Time Location Details
Friday 16-18 A6/SR 009 Seminarraum Übung 01

Diskrete Mathematik II - Optimierung W21/22
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Most Recent Announcement

2021-10-19:  Which DM I lectures are relevant for DM II - Optimization?

Dear students,

of course, they are all relevant, but a closer selection focuses on lectures 13 and 15--25.

Best, Ralf Borndörfer

 



Published by: Ralf Borndörfer
Older announcements

2021-10-19
Published by: Ralf Borndörfer
Onsite/Online Lectures (time corrected, vbrick link added)

Dear Students,

the lecture Discrete Mathematics II - Optimization will be an onsite lecture, but there will also be videos (see below).

Onsite, we are obliged to follow the Corona regime, which means that we must adhere to 3G. 

The easiest thing is to maintain a list of vaccinated people. My plan is to check that once in the first lecture, and then hopefully we will know each other, such we can resort to a normal operation mode afterwards.

It would be great if you were there tomorrow at 12:00, then we can do that before the actual start of the lecture at 12:15.

If everybody is 3G, it is allowed to drop masks, provided that we can keep 1,5 m distance. I don't know if that will be possible, we have to check that out tomorrow. So to be on the safe side, please bring your mask.

I will also continue with the videos in the DM I style and already uploaded the first two to vbrick (https://fu-berlin.eu.vbrickrev.com/). However, I don't promise that I will always be completely on time with them; I'll do my best.

Looking forward to seeing you tomorrow,

Ralf Borndörfer


Diskrete Mathematik II - Optimierung W21/22
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