5 citations · 9 across the 12 of their papers we have counts for
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Note on Minkowski Summation and Unimodularity in Discrete Convex Analysis
Kazuo Murota, Akihisa Tamura
This short note gives an elementary alternative proof for a theorem of Danilov and Koshevoy on Minkowski summation and unimodularity in discrete convex analysis. It is intended to…
Decomposition of an Integrally Convex Set into a Minkowski Sum of Bounded and Conic Integrally Convex Sets
Kazuo Murota, Akihisa Tamura
Every polyhedron can be decomposed into a Minkowski sum (or vector sum) of a bounded polyhedron and a polyhedral cone. This paper establishes similar statements for some classes of…
Shapley-Folkman-type Theorem for Integrally Convex Sets
Kazuo Murota, Akihisa Tamura
The Shapley-Folkman theorem is a statement about the Minkowski sum of (non-convex) sets, expressing the closeness of the Minkowski sum to convexity in a quantitative manner. This p…
Recent Progress on Integrally Convex Functions
Kazuo Murota, Akihisa Tamura
Integrally convex functions constitute a fundamental function class in discrete convex analysis, including M-convex functions, L-convex functions, and many others. This paper aims…
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…
Integrality of Subgradients and Biconjugates of Integrally Convex Functions
Kazuo Murota, Akihisa Tamura
Integrally convex functions constitute a fundamental function class in discrete convex analysis. This paper shows that an integer-valued integrally convex function admits an integr…
Scaling, Proximity, and Optimization of Integrally Convex Functions
Satoko Moriguchi, Kazuo Murota, Akihisa Tamura +1
In discrete convex analysis, the scaling and proximity properties for the class of L-convex functions were established more than a decade ago and have been used to desig…