Journal of the Operations Research Society of Japan
Online ISSN : 2188-8299
Print ISSN : 0453-4514
ISSN-L : 0453-4514
ON EQUIVALENCE OF M♮-CONCAVITY OF A SET FUNCTION AND SUBMODULARITY OF ITS CONJUGATE
Kazuo Murota , Akiyoshi Shioura
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Keywords: Combinatorial optimization, discrete convex analysis, M♮-concave function, valuated matroid, submodularity, conjugate function
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2018 Volume 61 Issue 2 Pages 163-171

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Abstract

A fundamental theorem in discrete convex analysis states that a set function is M♮-concave if and only if its conjugate function is submodular. This paper gives an alternative direct proof to this fact.

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© 2018 The Operations Research Society of Japan
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