Discrete convex functions are used in many areas, including operations research, discrete-event systems, game theory, and economics. The objective of this paper is to investigate basic operations such as direct sum, splitting, and aggregation that are related to network induction of discrete convex functions as well as discrete convex sets. Various kinds of discrete convex functions in discrete convex analysis are considered such as integrally convex functions, L-convex functions, M-convex functions, multimodular functions, and discrete midpoint convex functions.

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关于离散凸函数网络归纳的基本运算

离散凸函数用于许多领域，包括运筹学，离散事件系统，博弈论和经济学。本文的目的是研究与离散凸函数以及离散凸集的网络归纳相关的基本运算，例如直接和，分解和聚合。考虑了离散凸分析中的各种离散凸函数，例如积分凸函数，L-凸函数，M-凸函数，多模函数和离散中点凸函数。