A Bundle Approach for SDPs with Exact Subgraph Constraints [article]

Elisabeth Gaar, Franz Rendl
2019 arXiv   pre-print
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
more » ... 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.
arXiv:1902.05345v1 fatcat:ra4ckvzbdvaklpulpc5hzxhfdm