Course

MATH-504: Integer optimisation

Summary

The course aims to introduce the basic concepts and results of integer optimization with special emphasis on algorithmic problems on lattices that have proved to be important in theoretical computer science and cryptography during the past 30 years.

Lectures

Instructor

Friedrich Eisenbrand

Friedrich Eisenbrand's main research interests lie in the field of discrete optimization, in particular in algorithms and complexity, integer programming, geometry of numbers, and applied optimization. He is best known for his work on efficient algorithms for integer programming in fixed dimension and the theory of cutting planes, which are an important tool to solve large scale industrial optimization problems in practice. Before joining EPFL in March 2008, Friedrich Eisenbrand was a full professor of mathematics at the University of Paderborn. Friedrich received the Heinz Maier-Leibnitz award of the German Research Foundation (DFG) in 2004 and the Otto Hahn medal of the Max Planck Society in 2001.

Official source

https://edu.epfl.ch/coursebook/en/integer-optimisation-MATH-504

Moodle Page

http://go.epfl.ch/MATH-504

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Summary

Lectures

Instructor

Friedrich Eisenbrand

Official source

https://edu.epfl.ch/coursebook/en/integer-optimisation-MATH-504

Moodle Page

http://go.epfl.ch/MATH-504

About this result

Lectures in this course (31)

Transference Bounds

Explores transference bounds, ellipsoids, and determining the shortest vector.

2D Case: Polynomial Encroaching

Covers the 2D case of polynomial encroaching and vertices of polyhedra.

Integer Hull: General Case

Covers the concept of the integer hull in the general case, focusing on the proof of claim and the properties of cells.

Closest Vector Problem: Voronoi Cells

Explores the Closest Vector Problem and Voronoi cells in lattice reduction algorithms.

Voronoi Analysis: Closest Vector Problem

Explores Voronoi analysis for efficient Closest Vector Problem solutions.

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