Lecture: Introduction to Linear and Combinatorial Optimization (ADM I)

	Lecture: Introduction to Linear and Combinatorial Optimization (ADM I)
	Winter Semester 2012/2013

LV-Nr.: 3236 L 148

Prof. Dr. Dr. h.c. mult. Martin Grötschel and Dr. Benjamin Hiller

News Downloads Contents Registration Location and Timing Prerequisites Contact Literature Further Information

News

In the winter semester 2012/2013 I will jointly offer with Dr. Benjamin Hiller the lecture "Introduction to Linear and Combinatorial Optimization (ADM I)". This lecture is the first part of the lecture series "Algorithmic Discrete Mathematics (ADM)", which is given at the Institute of Mathematics of TU Berlin.
In the course, we will provide algorithmic and structural foundations of linear and combinatorial optimization. This includes basic notions from graph and polyhedra theory, techniques of algorithmic thinking and working, e.g., complexity of problem classes, the efficiency of algorithms and approximation which will be checked on examples of selected practical optimization problems.

Please, find here (in German only) the module description of the lecture ADM I.

News of previous lectures in this semester can be found in the archive.

Here are the news concerning the following lecture and exercises:

January 16, 2013:

Information about the final examination:
Instead of a final verbal examination to the lecture ADM I, a written exam will take place in the afternoon of February 15, 2013 (probably 14:15 o'clock in auditorium MA 041). Due to the big number of listeners verbal single checks are not practicable.

The first (pre)announcement:
To the lecture ADM II in the summer semester in 2013 an exam analogously takes place at the semester end.

The second (pre)announcement:
As a "special offer" I allow after ending of the (part) to cycle I/ADM II still a verbal check with the contents of both lectures. Nevertheless, this verbal check must be divided for juridical reasons in two parts. The first part is dedicated only ADM I and is concluded with own mark, then follows a verbal check about the contents of ADM II, and for this an independent mark must be as well awarded.

March 19, 2013:

The results of the written examination (of February 25, 2013) can be found here.

March 28, 2013:

You may have a look at your written exam on Thursday, April 4, 2013, 13:00-15:00 h, at TU Berlin, Mathematics Building, room MA 312.

April 4, 2013:

The final version of the lecture notes (version of March 26, 2013) can be downloaded (see Downloads).

Downloads

Downloads of previous lectures in this semester can be found in the archive.

Here you will find the current downloads of lecture notes and corresponding exercises.

April 4, 2013:

Please find here the final lecture notes (version of March 26, 2013) (in German only).

Brief introduction to the theory of graphs, digraphs and networks. Overview of issues and mathematical sub-areas of optimization, modeling of real-world problems arising in practice. Introduction to linear optimization: The structure and geometry of linear programs, duality theory, transformation to standard forms, bases, primal and dual feasibility.
Detailed description of the simplex method in its basic version, geometric interpretation.
Polynomial algorithms for basic problems in combinatorial optimization explained on examples: spanning trees, shortest paths, maximum flows, minimum cost flows, etc.
In addition, the basics of complexity theory will be presented: the classes P and NP, NP-completeness.
Examples will be given for NP-hard problems (cliques, traveling salesman, maximum cut and coloring problems).

Registration

Students are requested to register during the first lecture (please fill in the circulating list your name, first name, email address, study course, registration number (Matrikelnummer) of your university).

Location and Timing

The lecture will take place at: TU Berlin, Math building, lecture halls MA 041 or MA 043 (depending on timing).

Two classes per week, on:
Wednesday, 10:00 - 12:00 h (October 24 - February 16, 2013), lecture hall MA 041
Thursday, 16:00 - 18:00 h (October 18 - February 16, 2013), lecture hall MA 043

First lecture will take place on: Thursday, October 18, 2012 at TU Berlin, Math building, lecture hall MA 043, 16:15 h.

Exercise sessions: on Fridays, 14:00 - 16:00 h, MA 041 (responsible: Torsten Klug, Zuse Institute Berlin, email: klug@zib.de).

First session: Friday, October 19, 2012 at TU Berlin, Math building, room MA 041, 14:15 h.

Tutorials:

Monday,	12:00 - 14:00 h,	Room: MA 651
Tuesday,	08:00 - 10:00 h,	Room: MA 651
Wednesday,	12:00 - 14:00 h,	Room: MA 751

Tutor: Veit Wiechert (TU Berlin, Email: wiechert@math.tu-berlin.de).

Prerequisites

Knowledge in analysis, linear algebra, and programming is expected.

Contact

Office	Name	Consultation-hours	Room	Phone	Email
Office at TU Berlin:	Martin Grötschel	on appointment	Room: MA 302	314-23266	Please use: groetschelzib.de
Office at Zuse Institute:	Martin Grötschel	on appointment	Room: 3025	84185-210	groetschel $Beschreibung: C:\Users\groetsch\Desktop\klammeraffe.gif$ zib.de
Office Zuse Institute:	Benjamin Hiller	on appointment	Room: 3101	84185-406	hillerzib.de
Tutor: Office at TU	Veit Wiechert	on appointment	Room: MA 613	314-28708	wiechertmath.tu-berlin.de

Literature

Here are some proposals concerning the literature on linear and combinatorial optimization, and graph theory as well:

George B. Dantzig: Lineare Programmierung und Erweiterungen. Springer-Verlag, 1966.
M. Grötschel, L. Lovász, A. Schrijver, Geometric Algorithms and Combinatorial Optimization. Springer, 1988.
Ravindra K. Ahuja, Thomas L. Magnanti, James B. Orlin: Network flows: theory, algorithms, and applications, Prentice Hall, 1993.
M. Padberg, Linear Optimization and Extensions, Springer, 1995.
A. Schrijver, Theory of Linear and Integer Programming, Wiley, 1998.
Christos H. Papadimitriou, Kenneth Steiglitz: Combinatorial Optimization: Algorithms and Complexity, 1998.
George L. Nemhauser, Laurence A. Wolsey: Integer and Combinatorial Optimization, Wiley, 1999.
Reinhard Diestel, Graph Theory, Second Edition, Springer, 2000.
R. J. Vanderbei, Linear Programming, Springer, 2001.
Robert Bixby: Solving real-world linear programs: A decade and more of progress. In: Operations Research, Band 50, Nr. 1, 2002, S. 3–15.
Dimitris Bertsimas, Robert Weismantel: Optimization Over Integers , 2005.
J. Matousek, B. Gärtner, Using and Understanding Linear Programming, Springer, 2006.
Sven Oliver Krumke, Hartmut Noltemeier: Graphentheoretische Konzepte und Algorithmen, Teubner, 2006.
Bernhard Korte, Jens Vygen: Combinatorial Optimization Theory and Algorithms, Springer, 2000 - 2012.
New: D. Jungnickel, Graphs, Networks and Algorithms, Series: Algorithms and Computation in Mathematics, Volume 5, fourth edition, Springer, 2013
Peter Gritzmann, Grundlagen der Mathematischen Optimierung, Springer Spektrum, 2013

Further Information

The lecture is classified as a course with 10 ECTS credit points.

Criteria for the scientific acquisition:
We will distribute a total of 14 notes with exercises (there will be 2 series of 7 exercise sheets). You have to get at least 50 % of the exercise points in series one and two, respectively.

Information about the final examination: Instead of a final verbal examination to the lecture ADM I, a written exam will take place in the afternoon of February 15, 2013 (probably 14:15 o'clock in auditorium MA 041). Due to the big number of listeners verbal single checks are not practicable. The first (pre)announcement: To the lecture ADM II in the summer semester in 2013 an exam analogously takes place at the semester end. The second (pre)announcement: As a "special offer" I allow after ending of the (part) to cycle I/ADM II still a verbal check with the contents of both lectures. Nevertheless, this verbal check must be divided for juridical reasons in two parts. The first part is dedicated only ADM I and is concluded with own mark, then follows a verbal check about the contents of ADM II, and for this an independent mark must be as well awarded.

Last changes: April 4, 2013