Integer Programming and Algorithmic Geometry of Numbers: A tutorial
F Eisenbrand - 50 Years of Integer Programming 1958-2008: From the …, 2010 - Springer
This chapter surveys a selection of results from the interplay of integer programming and the
geometry of numbers. Apart from being a survey, the text is also intended as an entry point …
geometry of numbers. Apart from being a survey, the text is also intended as an entry point …
Integer programming, lattices, and results in fixed dimension
K Aardal, F Eisenbrand - … in Operations Research and Management Science, 2005 - Elsevier
We review and describe several results regarding integer programming problems in fixed
dimension. First, we describe various lattice basis reduction algorithms that are used as …
dimension. First, we describe various lattice basis reduction algorithms that are used as …
Logahedra: A new weakly relational domain
Weakly relational numeric domains express restricted classes of linear inequalities that
strike a balance between what can be described and what can be efficiently computed …
strike a balance between what can be described and what can be efficiently computed …
Lifting for the integer knapsack cover polyhedron
We consider the integer knapsack cover polyhedron which is the convex hull of the set
consisting of n-dimensional nonnegative integer vectors that satisfy one linear constraint …
consisting of n-dimensional nonnegative integer vectors that satisfy one linear constraint …
On the exact separation of mixed integer knapsack cuts
R Fukasawa, M Goycoolea - Mathematical programming, 2011 - Springer
During the last decades, much research has been conducted on deriving classes of valid
inequalities for mixed integer knapsack sets, which we call knapsack cuts. Bixby et al.(The …
inequalities for mixed integer knapsack sets, which we call knapsack cuts. Bixby et al.(The …
On minimum integer representations of weighted games
We study minimum integer representations of weighted games, ie representations where the
weights are integers and every other integer representation is at least as large in each …
weights are integers and every other integer representation is at least as large in each …
Mirror-descent methods in mixed-integer convex optimization
M Baes, T Oertel, C Wagner, R Weismantel - Facets of Combinatorial …, 2013 - Springer
In this paper, we address the problem of minimizing a convex function f over a convex set,
with the extra constraint that some variables must be integer. This problem, even when f is a …
with the extra constraint that some variables must be integer. This problem, even when f is a …
[PDF][PDF] Integer convex minimization in low dimensions
T Oertel - 2014 - research-collection.ethz.ch
Integer Convex Minimization in Low Dimensions Page 1 DISS. ETH NO. 22288 Integer Convex
Minimization in Low Dimensions A thesis submitted to attain the degree of DOCTOR OF …
Minimization in Low Dimensions A thesis submitted to attain the degree of DOCTOR OF …
The LLL algorithm and integer programming
K Aardal, F Eisenbrand - The LLL Algorithm: Survey and Applications, 2009 - Springer
The LLL Algorithm and Integer Programming Page 1 Chapter 9 The LLL Algorithm and Integer
Programming Karen Aardal and Friedrich Eisenbrand Abstract The LLL algorithm has proven …
Programming Karen Aardal and Friedrich Eisenbrand Abstract The LLL algorithm has proven …
Split cuts in the plane
Split Cuts in the Plane Page 1 Copyright © by SIAM. Unauthorized reproduction of this article is
prohibited. SIAM J. OPTIM. © 2021 Society for Industrial and Applied Mathematics Vol. 31, No …
prohibited. SIAM J. OPTIM. © 2021 Society for Industrial and Applied Mathematics Vol. 31, No …