Discrete Fenchel duality for a pair of integrally convex and separable convex functions

Abstract Discrete Fenchel duality is one of the central issues in discrete convex analysis. The Fenchel-type min–max theorem for a pair integer-valued M $$^{\natural }$$ ♮ -convex functions generalizes formulas polymatroid intersection and valuated matroid intersection. In this paper we establish formula integrally separable functions. Integrally constitute fundamental function class analysis, including both L functions, whereas are characterized as those which -convex. proved by revealing kind box integrality subgradients an function. proof based on Fourier–Motzkin elimination.