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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.OC2020
Directed Discrete Midpoint Convexity
Akihisa Tamura, Kazuya Tsurumi
For continuous functions, midpoint convexity characterizes convex functions. By considering discrete versions of midpoint convexity, several types of discrete convexities of functi…