10 citations · 45 across the 35 of their papers we have counts for
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Inclusion and Intersection Relations Between Fundamental Classes of Discrete Convex Functions
Satoko Moriguchi, Kazuo Murota
In discrete convex analysis, various convexity concepts are considered for discrete functions such as separable convexity, L-convexity, M-convexity, integral convexity, and multimo…
Note on the Polyhedral Description of the Minkowski Sum of Two L-convex Sets
Satoko Moriguchi, Kazuo Murota
L-convex sets are one of the most fundamental concepts in discrete convex analysis. Furthermore, the Minkowski sum of two L-convex sets, called L2-convex sets, is an intriguing obj…
Discrete Fenchel Duality for a Pair of Integrally Convex and Separable Convex Functions
Kazuo Murota, Akihisa Tamura
Discrete Fenchel duality is one of the central issues in discrete convex analysis. The Fenchel-type min-max theorem for a pair of integer-valued M-natural-convex functions generali…
Exchange Properties of M-natural-concave Set Functions and Valuated Matroids
Kazuo Murota
This is a survey article on the exchange properties characterizing M-natural-concave set functions and valuated matroids (M-concave set functions). The objective of this paper is t…