论文标题
在整合凸功能上的最新进展
Recent Progress on Integrally Convex Functions
论文作者
论文摘要
在离散凸分析中，凸功能的积分构成了一个基本函数类别，包括M-Convex函数，L-Convex函数和许多其他功能。本文的目的是针对以一些新的技术结果进行整体凸起功能的最新结果进行了相当全面的调查。本文所涵盖的主题包括积分凸集和功能的特征，对积分凸组和功能的操作，使用接近度尺寸的算法最小化的最佳标准，积分双缀合性以及离散的Fenchel二元性。尽管M-Convex和L-Convex函数的理论已经建立在对矩形和子管函数的基本结果的基础上，但开发积分传达函数的理论需要更通用和基本工具，例如傅立叶 - 莫茨金消除。
Integrally convex functions constitute a fundamental function class in discrete convex analysis, including M-convex functions, L-convex functions, and many others. This paper aims at a rather comprehensive survey of recent results on integrally convex functions with some new technical results. Topics covered in this paper include characterizations of integral convex sets and functions, operations on integral convex sets and functions, optimality criteria for minimization with a proximity-scaling algorithm, integral biconjugacy, and the discrete Fenchel duality. While the theory of M-convex and L-convex functions has been built upon fundamental results on matroids and submodular functions, developing the theory of integrally convex functions requires more general and basic tools such as the Fourier-Motzkin elimination.
