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子模性与离散凸性
Submodularity and Discrete Convexity |
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| 课程网址: |
http://videolectures.net/nipsworkshops2012_fujishige_submodularit...
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| 主讲教师: |
Satoru Fujishige
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| 开课单位: |
京都大学
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| 开课时间: |
2013-01-16
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| 课程语种: |
日语
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| 中文简介: |
本讲是一个教程，给出了子模函数和离散凸性的一些本质。我的演讲内容如下：＃子模和超模函数##子模块##分配格和集（Birkhoff Iri）#Submodular系统和超模系统##子模多面体和基多面体##对偶##多面体和拟阵##广义多面体##边缘矢量表征##交叉和相交子模函数＃交叉定理及其等价##交叉定理##离散分离定理＃ ＃Fenchel对偶定理## Minkowski和定理＃最小标准基数和子模块函数最小化## Lexicographically Optimal Base ##最小标准基数##子模块函数最小化＃最大权重基础问题##贪心算法## Lovasz扩展## Subgradients和Subdifferentials子模函数#Discrete Convex A.分析##L♮凸函数##M♮凸函数##离散分离定理## Fenchel对偶定理
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| 课程简介: |
The present talk is a tutorial one and gives some essence of submodular functions and discrete convexity. The contents of my talk will be the following: # Submodular and Supermodular Functions ## Submodularity ## Distributive Lattices and Posets (Birkhoff-Iri) # Submodular Systems and Supermodular Systems ## Submodular polyhedron and Base Polyhedron ## Duality ## Polymatroids and Matroids ## Generalized Polymatroids ## Characterization by Edge-vectors ## Crossing- and Intersecting-submodular Functions # Intersection Theorem and Its Equivalents ## Intersection Theorem ## Discrete Separation Theorem ## Fenchel Duality Theorem ## Minkowski Sum Theorem # Minimum-Norm Base and Submodular Function Minimization ## Lexicographically Optimal Base ## Minimum-Norm Base ## Submodular Function Minimization # Maximum Weight Base Problem ## Greedy Algorithm ## Lovasz extension ## Subgradients and Subdifferentials of Submodular Functions # Discrete Convex Analysis ## L♮-convex Functions ## M♮-convex Functions ## Discrete Separation Theorem ## Fenchel Duality Theorem
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| 关 键 词: |
子模函数; 离散凸性; 超模函数
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| 课程来源: |
视频讲座网
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| 最后编审: |
2019-09-08：lxf
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| 阅读次数: |
183
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