A Polyhedral Approach to Bisubmodular Function Minimization
Optimization and Control
2020-09-30 v3 Discrete Mathematics
Abstract
We consider minimization problems with bisubmodular objective functions. We propose valid inequalities, namely the poly-bimatroid inequalities, and provide a complete linear description of the convex hull of the epigraph of a bisubmodular function. Furthermore, we develop a cutting plane algorithm for constrained bisubmodular minimization based on the poly-bimatroid inequalities. Our computational experiments on the minimization subproblem in robust coupled sensor placement show that our algorithm can solve highly non-linear problems that do not admit compact mixed-integer linear formulations.
Cite
@article{arxiv.2003.06036,
title = {A Polyhedral Approach to Bisubmodular Function Minimization},
author = {Qimeng Yu and Simge Kucukyavuz},
journal= {arXiv preprint arXiv:2003.06036},
year = {2020}
}