A Bundle Approach for SDPs with Exact Subgraph Constraints
Abstract
The 'exact subgraph' approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational challenge because of the potentially large number of violated subgraph constraints. We introduce a computational framework for these relaxations designed to cope with these difficulties. We suggest a partial Lagrangian dual, and exploit the fact that its evaluation decomposes into two independent subproblems. This opens the way to use the bundle method from non-smooth optimization to minimize the dual function. Computational experiments on the Max-Cut, stable set and coloring problem show the efficiency of this approach.
Cite
@article{arxiv.1902.05345,
title = {A Bundle Approach for SDPs with Exact Subgraph Constraints},
author = {Elisabeth Gaar and Franz Rendl},
journal= {arXiv preprint arXiv:1902.05345},
year = {2019}
}