Inclusion and Intersection Relations Between Fundamental Classes of Discrete Convex Functions
Abstract
In discrete convex analysis, various convexity concepts are considered for discrete functions such as separable convexity, L-convexity, M-convexity, integral convexity, and multimodularity. These concepts of discrete convex functions are not mutually independent. For example, M-natural-convexity is a special case of integral convexity, and the combination of L-natural-convexity and M-natural-convexity coincides with separable convexity. This paper aims at a fairly comprehensive analysis of the inclusion and intersection relations for various classes of discrete convex functions. Emphasis is put on the analysis of multimodularity in relation to L-natural-convexity and M-natural-convexity.
Cite
@article{arxiv.2111.07240,
title = {Inclusion and Intersection Relations Between Fundamental Classes of Discrete Convex Functions},
author = {Satoko Moriguchi and Kazuo Murota},
journal= {arXiv preprint arXiv:2111.07240},
year = {2023}
}
Comments
36 pages. arXiv admin note: text overlap with arXiv:1907.09161