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 …

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 …

Logahedra: A new weakly relational domain

JM Howe, A King - International Symposium on Automated Technology for …, 2009 - Springer
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 …

Lifting for the integer knapsack cover polyhedron

WK Chen, L Chen, YH Dai - Journal of Global Optimization, 2023 - Springer
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 …

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 …

On minimum integer representations of weighted games

J Freixas, S Kurz - Mathematical Social Sciences, 2014 - Elsevier
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 …

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 …

[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 …

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 …

Split cuts in the plane

A Basu, M Conforti, M Di Summa, H Jiang - SIAM Journal on Optimization, 2021 - SIAM
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 …