# Active-set Methods for Submodular Minimization Problems

@article{Kumar2017ActivesetMF, title={Active-set Methods for Submodular Minimization Problems}, author={K. S. Sesh Kumar and Francis R. Bach}, journal={J. Mach. Learn. Res.}, year={2017}, volume={18}, pages={132:1-132:31} }

We consider the submodular function minimization (SFM) and the quadratic minimization problemsregularized by the Lov'asz extension of the submodular function. These optimization problemsare intimately related; for example,min-cut problems and total variation denoising problems, wherethe cut function is submodular and its Lov'asz extension is given by the associated total variation.When a quadratic loss is regularized by the total variation of a cut function, it thus becomes atotal variation… Expand

#### 6 Citations

Fast Decomposable Submodular Function Minimization using Constrained Total Variation

- Mathematics, Computer Science
- NeurIPS
- 2019

A modified convex problem requiring constrained version of the total variation oracles that can be solved with significantly fewer calls to the simple minimization oracles is considered. Expand

Stochastic Submodular Maximization: The Case of Coverage Functions

- Computer Science, Mathematics
- NIPS
- 2017

This model captures situations where the discrete objective arises as an empirical risk, or is given as an explicit stochastic model, and yields solutions that are guaranteed to match the optimal approximation guarantees, while reducing the computational cost by several orders of magnitude, as demonstrated empirically. Expand

Optimization of Graph Total Variation via Active-Set-based Combinatorial Reconditioning

- Computer Science, Mathematics
- AISTATS
- 2020

This work proposes a novel adaptive preconditioner driven by a sharp analysis of the local linear convergence rate depending on the "active set" at the current iterate, and shows that nested-forest decomposition of the inactive edges yields a guaranteed locallinear convergence rate. Expand

Differentiable Learning of Submodular Models

- Mathematics
- NIPS 2017
- 2017

Can we incorporate discrete optimization algorithms within modern machine learning models? For example, is it possible to use in deep architectures a layer whose output is the minimal cut of a… Expand

Submodular Kernels for Efficient Rankings

- Computer Science, Mathematics
- ArXiv
- 2021

This work exploits geometric structure of ranked data and additional available information about the objects to derive a submodular kernel that drastically reduces the computational cost compared to state-of-the-art kernels and scales well to large datasets while attaining good empirical performance. Expand

Novel applications of intelligent computing paradigms for the analysis of nonlinear reactive transport model of the fluid in soft tissues and microvessels

- Computer Science
- Neural Computing and Applications
- 2019

The methodology integrates the artificial neural network, genetic algorithms, and pattern search aided by active-set technique (AST) and interior-point technique (IPT) to solve a one-dimensional steady-state nonlinear reactive transport model (RTM) that is meant for fluid and solute transport model of soft tissues and microvessels. Expand

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