LP approximations to mixed-integer polynomial optimization problems
Abstract
We present a class of linear programming approximations for constrained optimization problems. In the case of mixed-integer polynomial optimization problems, if the intersection graph of the constraints has bounded tree-width our construction yields a class of linear size formulations that attain any desired tolerance. As a result, we obtain an approximation scheme for the "AC-OPF" problem on graphs with bounded tree-width. We also describe a more general construction for pure binary optimization problems where individual constraints are available through a membership oracle; if the intersection graph for the constraints has bounded tree-width our construction is of linear size and exact. This improves on a number of results in the literature, both from the perspective of formulation size and generality.
Cite
@article{arxiv.1501.00288,
title = {LP approximations to mixed-integer polynomial optimization problems},
author = {Daniel Bienstock and Gonzalo Munoz},
journal= {arXiv preprint arXiv:1501.00288},
year = {2016}
}