# Reflection methods for user-friendly submodular optimization

arXiv: https://arxiv.org/abs/1311.4296 · HTML: https://mlsanity.com/paper/1311.4296/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Nov 2013.

## Built on by (most cited first, 11 of 11)

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- [Fast, Differentiable and Sparse Top-k: a Convex Analysis Perspective](https://mlsanity.com/paper/2302.01425/) (2023)
- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [Decomposable Submodular Function Minimization via Maximum Flow](https://mlsanity.com/paper/2103.03868/) (2021)
- [Modeling Edge-Specific Node Features through Co-Representation Neural Hypergraph Diffusion](https://mlsanity.com/paper/2405.14286/) (2024)
- [Minimisation of Submodular Functions Using Gaussian Zeroth-Order Random Oracles](https://mlsanity.com/paper/2510.15257/) (2025)
- [Solving the Offline and Online Min-Max Problem of Non-smooth Submodular-Concave Functions: A Zeroth-Order Approach](https://mlsanity.com/paper/2601.21243/) (2026)
- [Approximate Decomposable Submodular Function Minimization for Cardinality-Based Components](https://mlsanity.com/paper/2110.14859/) (2021)
- [Hypergraphs with Edge-Dependent Vertex Weights: p-Laplacians and Spectral Clustering](https://mlsanity.com/paper/2208.07457/) (2022)
- [Avoiding Exponential Blow-Up in Distributive Lattice Submodular Minimization](https://mlsanity.com/paper/2606.14764/) (2026)

## Abstract (arXiv)

Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular functions, especially for minimization problems. While general submodular minimization is challenging, we propose a new method that exploits existing decomposability of submodular functions. In contrast to previous approaches, our method is neither approximate, nor impractical, nor does it need any cumbersome parameter tuning. Moreover, it is easy to implement and parallelize. A key component of our method is a formulation of the discrete submodular minimization problem as a continuous best approximation problem that is solved through a sequence of reflections, and its solution can be easily thresholded to obtain an optimal discrete solution. This method solves both the continuous and discrete formulations of the problem, and therefore has applications in learning, inference, and reconstruction. In our experiments, we illustrate the benefits of our method on two image segmentation tasks.