# Structured Convex Optimization under Submodular Constraints

arXiv: https://arxiv.org/abs/1309.6850 · HTML: https://mlsanity.com/paper/1309.6850/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2013.

## Built on by (most cited first, 1 of 1)

- [Upper Entropy for 2-Monotone Lower Probabilities](https://mlsanity.com/paper/2603.23558/) (2026)

## Abstract (arXiv)

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.