Recent progress on integrally convex functions

Abstract Integrally convex functions constitute a fundamental function class in discrete analysis, including M-convex functions, L-convex and many others. This paper aims at rather comprehensive survey of recent results on integrally with some new technical results. Topics covered this include characterizations integral sets operations optimality criteria for minimization proximity-scaling algorithm, biconjugacy, the Fenchel duality. While theory has been built upon matroids submodular developing requires more general basic tools such as Fourier–Motzkin elimination.