# Polyhedral aspects of Submodularity, Convexity and Concavity

@article{Iyer2015PolyhedralAO, title={Polyhedral aspects of Submodularity, Convexity and Concavity}, author={Rishabh K. Iyer and Jeff A. Bilmes}, journal={ArXiv}, year={2015}, volume={abs/1506.07329} }

Seminal work by Edmonds and Lovasz shows the strong connection between submodularity and convexity. Submodular functions have tight modular lower bounds, and subdifferentials in a manner akin to convex functions. They also admit poly-time algorithms for minimization and satisfy the Fenchel duality theorem and the Discrete Seperation Theorem, both of which are fundamental characteristics of convex functions. Submodular functions also show signs similar to concavity. Submodular maximization…

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