# 401-3901-00L Mathematical Optimization

Semester | Autumn Semester 2017 |

Lecturers | R. Weismantel |

Periodicity | yearly course |

Language of instruction | English |

### Catalogue data

Abstract | Mathematical treatment of diverse optimization techniques. |

Objective | Advanced optimization theory and algorithms. |

Content | 1) Linear optimization: The geometry of linear programming, the simplex method for solving linear programming problems, Farkas' Lemma and infeasibility certificates, duality theory of linear programming. 2) Nonlinear optimization: Lagrange relaxation techniques, Newton method and gradient schemes for convex optimization. 3) Integer optimization: Ties between linear and integer optimization, total unimodularity, complexity theory, cutting plane theory. 4) Combinatorial optimization: Network flow problems, structural results and algorithms for matroids, matchings, and, more generally, independence systems. |

Literature | 1) D. Bertsimas & R. Weismantel, "Optimization over Integers". Dynamic Ideas, 2005. 2) A. Schrijver, "Theory of Linear and Integer Programming". John Wiley, 1986. 3) D. Bertsimas & J.N. Tsitsiklis, "Introduction to Linear Optimization". Athena Scientific, 1997. 4) Y. Nesterov, "Introductory Lectures on Convex Optimization: a Basic Course". Kluwer Academic Publishers, 2003. 5) C.H. Papadimitriou, "Combinatorial Optimization". Prentice-Hall Inc., 1982. |

Prerequisites / Notice | Linear algebra. |

### Performance assessment

Performance assessment information (valid until the course unit is held again) | |

Performance assessment as a semester course | |

ECTS credits | 11 credits |

Examiners | R. Weismantel |

Type | session examination |

Language of examination | English |

Course attendance confirmation required | No |

Repetition | The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit. |

Mode of examination | written 120 minutes |

Written aids | 10 one-sided A4 sheets or 5 two-sided A4 sheets, hand- or typewritten. |

This information can be updated until the beginning of the semester; information on the examination timetable is binding. |

### Learning materials

Main link | Course Website |

Moodle course | Exercise sheets and all information on the course |

Additional links | Information on other courses offered at IFOR |

Only public learning materials are listed. |

### Courses

Number | Title | Hours | Lecturers | |||||||
---|---|---|---|---|---|---|---|---|---|---|

401-3901-00 V | Mathematical Optimization | 4 hrs |
| R. Weismantel | ||||||

401-3901-00 U | Mathematical Optimization | 2 hrs |
| R. Weismantel |

### Restrictions

There are no additional restrictions for the registration. |