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Maximizing a <inline-formula><tex-math id="M1">$ k $</tex-math></inline-formula>-submodular function with <inline-formula><tex-math id="M2">$ p $</tex-math></inline-formula>-system constraints

Hanlu Ye, Min Li, Yang Zhou, Qian Liu
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Submodular function minimization and polarity [PDF]

Mathematical Programming, 2021
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 Lovász extension. The polar approach provides an alternative proof for the convex hull description of the epigraph of a submodular function ...
Alper Atamturk
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Submodular function minimization

Mathematical Programming, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Satoru Iwata
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Submodular Functions and Rooted Trees

Theory of Computing Systems, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yaokun Wu, Yinfeng Zhu 0001
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Decomposition of submodular functions

Combinatorica, 1983
A decomposition theory for submodular functions is described. Any such function is shown to have a unique decomposition consisting of indecomposable functions and certain highly decomposable functions, and the latter are completely characterized. Applications include decompositions of hypergraphs based on edge and vertex connectivity, the decomposition
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On the subdifferential of a submodular function

Mathematical Programming, 1984
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On submodular function minimization

Combinatorica, 1985
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Submodular functions and convexity

1983
In “continuous” optimization convex functions play a central role. Besides elementary tools like differentiation, various methods for finding the minimum of a convex function constitute the main body of nonlinear optimization. But even linear programming may be viewed as the optimization of very special (linear) objective functions over very special ...
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Minimizing a Submodular Function on a Lattice

Operations Research, 1978
This paper gives general conditions under which a collection of optimization problems, with the objective function and the constraint set depending on a parameter, has optimal solutions that are an isotone function of the parameter. Relating to this, we present a theory that explores and elaborates on the problem of minimizing a submodular function on
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