Distances of optimal solutions of mixed-integer programs
Optimization and Control
2018-01-29 v1
Abstract
A classic result of Cook et al. (1986) bounds the distances between optimal solutions of mixed-integer linear programs and optimal solutions of the corresponding linear relaxations. Their bound is given in terms of the number of variables and a parameter , which quantifies sub-determinants of the underlying linear inequalities. We show that this distance can be bounded in terms of and the number of integer variables rather than the total number of variables. To this end, we make use of a result by Olson (1969) in additive combinatorics and demonstrate how it implies feasibility of certain mixed-integer linear programs. We conjecture that our bound can be improved to a function that only depends on , in general.
Cite
@article{arxiv.1801.08751,
title = {Distances of optimal solutions of mixed-integer programs},
author = {Joseph Paat and Robert Weismantel and Stefan Weltge},
journal= {arXiv preprint arXiv:1801.08751},
year = {2018}
}