# Optimization

## Core Course, 4+2

# Basic Information

Lecturer: | Andreas Karrenbauer |
---|---|

Lectures: | Tuesday + Thursday, 14:00 - 16:00, E1.3 HS003; first lecture on Apr 20 |

Teaching Assistant: | Bojana Kodric |

Tutors: | Sören Bund-Becker, Davis Issac, Pavel Kolev |

Tutorials: | Mondays 10-12, E1.4 024, Sören Wednesdays 12-14, E1.4 024, Davis Fridays 12-14, E1.4 024, Pavel |

Credits: | 9 |

Prerequisites: | Basics in linear algebra, discrete mathematics, calculus, algorithms, and complexity. At Saarland University these topics are covered in the bachelor courses Mathematik für Informatiker 1 & 2, Grundzüge der Theoretischen Informatik, and Grundzüge von Algorithmen und Datenstrukturen. |

Exam: | Your final grade will be the best of the final exam and the re-exam. You may bring one A4 cheat sheet (double-sided, in your own handwriting) to the exams. |

If you want to participate in the course, please register to our mailing list!

# Description

This course provides an introduction to fundamental concepts and algorithmic methods for solving linear and integer linear programs.

Linear optimization is a key subject in theoretical computer science. Moreover, it has many applications in practice. A lot of problems can be formulated as (integer) linear optimization problem. For example, combinatorial problems, such as shortest paths, maximum flows, maximum matchings in graphs, among others have a natural formulation as a linear (integer) optimization problem. In this course you will learn:

- how to optimize a linear function subject to linear constraints
- how to formulate combinatorial problems as (integer) linear optimization problems
- how to solve them

To this end, basic concepts from polyhedral theory will be introduced. The simplex algorithm and the ellipsoid method will be presented. The lecture concludes with exact and approximation algorithms for NP-hard optimization problems. There will be theoretical and practical exercises.

# Policies

This is a 9-credit-point core lecture ("Stammvorlesung"). There will be two lectures and one exercise session per week. We will hand out exercises every week (usually worth 40 points) and each student should score at least 50% in the first half of the course (first 6 exercise sheets) and 50% in the second half in order to be allowed to take the exam.

Students will also have the chance to gather points by contributing to a wiki. Bonus points will be awarded for contributions to the wiki, i.e., for

- correction of typos
- fixing flaws
- filling gaps

The number of awarded bonus points will be determined in the following way: 10 points per 1k characters, further multiplied with a quality factor between 0 and 1.

# Lectures

# Literature

Good textbook on the topic include:

*Integer Programming*by Laurence A. Wolsey.*Introduction to Linear Optimization*by Dimitris Bertsimas and John N. Tsitsiklis.