Structured Convex Optimization under Submodular Constraints
Kiyohito Nagano, Yoshinobu Kawahara
A number of discrete and continuous optimization problems in machine learning are related to convex minimization problems under submodular constraints. In this paper, we deal with a submodular function with a directed graph structure, and we show that a wide range of convex optimization problems under submodular constraints can be solved much more efficiently than general submodular optimization methods by a reduction to a maximum flow problem. Furthermore, we give some applications, including sparse optimization methods, in which the proposed methods are effective. Additionally, we evaluate the performance of the proposed method through computational experiments.
PDF Link: /papers/13/p459-nagano.pdf
AUTHOR = "Kiyohito Nagano
and Yoshinobu Kawahara",
TITLE = "Structured Convex Optimization under Submodular Constraints",
BOOKTITLE = "Proceedings of the Twenty-Ninth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-13)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2013",
PAGES = "459--468"