A Note on Submodularity Preserved Involving the Rank Functions  

作　　者：Min Li Dong-Lei Du Da-Chuan Xu Zhen-Ning Zhang 

机构地区：[1]School of Mathematics and Statistics,Shandong Normal University,Jinan 250358,China [2]Faculty of Business Administration,University of New Brunswick,Fredericton,Canada [3]College of Applied Sciences,Beijing University of Technology,Beijing 100124,China

出　　处：《Journal of the Operations Research Society of China》2019年第3期399-407,共9页中国运筹学会会刊（英文）

基　　金：supported by Higher Educational Science and Technology Program of Shandong Province(No.J17KA171);Natural Science and Engineering Research Council of Canada(No.06446);the National Natural Science Foundation of China(No.11871081);Science and Technology Program of Beijing Education Commission(No.KM201810005006).

摘　　要：In many kinds of games with economic significance,it is very important to study the submodularity of functions.In this paper,wemainly study the problem of maximizing a concave function over an intersection of two matroids.We obtain that the submod-ularity may not be preserved,but it involves one maximal submodular problem(or minimal supermodular problem)with some conditions.Moreover,we also present examples showing that these conditions can be satisfied.

关 键 词：MATROID Submodular function Rank function Convexclosure GAME 

分 类 号：X70[环境科学与工程—环境工程]