3 papers
math.OC2025
Two Proofs of a Structural Theorem of Decreasing Minimization on Integrally Convex Sets
Kazuo Murota, Akihisa Tamura
This paper gives two different proofs to a structural theorem of decreasing minimization (lexicographic optimization) on integrally convex sets. The theorem states that the set of…
math.CO2024
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…
math.CO2024
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…