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arXiv · 1912.13238

Submodular Function Minimization and Polarity

Alper Atamturk·Vishnu Narayanan
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Abstract

Using polarity, we give an outer polyhedral approximation for the epigraph of set functions. For a submodular function, we prove that the corresponding polar relaxation is exact; hence, it is equivalent to the Lov\'asz extension. The polar approach provides an alternative proof for the convex hull description of the epigraph of a submodular function. Computational experiments show that the inequalities from outer approximations can be effective as cutting planes for solving submodular as well as non-submodular set function minimization problems.

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Alper Atamturk, Vishnu Narayanan. 2019-12-31. Submodular Function Minimization and Polarity. https://arxiv.org/abs/1912.13238

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