Mixed-integer Quadratic Programming is in NP
Discrete Mathematics
2014-07-21 v1 Combinatorics
Abstract
Mixed-integer quadratic programming is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral. In this paper, we prove that the decision version of mixed-integer quadratic programming is in NP, thereby showing that it is NP-complete. This is established by showing that if the decision version of mixed-integer quadratic programming is feasible, then there exists a solution of polynomial size. This result generalizes and unifies classical results that quadratic programming is in NP and integer linear programming is in NP.
Cite
@article{arxiv.1407.4798,
title = {Mixed-integer Quadratic Programming is in NP},
author = {Alberto Del Pia and Santanu S. Dey and Marco Molinaro},
journal= {arXiv preprint arXiv:1407.4798},
year = {2014}
}