Supporting hyperplane
转自：http://en.wikipedia.org/wiki/Supporting_hyperplane
Supporting hyperplane is a concept in geometry. A hyperplane divides a space into two half-spaces. A hyperplane is said to support a set S in Euclidean space 
if it meets both of the following:
- S is entirely contained in one of the two closed half-spaces determined by the hyperplane
- S has at least one point on the hyperplane.
Here, a closed half-space is the half-space that includes the hyperplane.
Supporting hyperplane theorem
This theorem states that if S is a closed convex set in a topological vector space X, and x0 is a point on the boundary of S, then there exists a supporting hyperplane containing x0. If 
(the dual space of X) such that 
for all 
, then
defines a supporting hyperplane.[1]
Conversely, if S is a closed set with nonempty interior such that every point has a supporting hyperplane, then S is a convex set.[1]
The hyperplane in the theorem may not be unique, as noticed in the second picture on the right. If the closed set S is not convex, the statement of the theorem is not true at all points on the boundary of S, as illustrated in the third picture on the right.
A related result is the separating hyperplane theorem.
Supporting hyperplane相关推荐
- Convex Optimization: 2 Convex sets
本篇为凸优化的课程笔记. 文章目录 Affine set 仿射集 Convex set 凸集 Convex combination and convex hull 凸组合与凸包 Convex cone ...
- 运筹系列30：COIN_OR优化套装
1. 介绍 COIN-OR是 Operations Research Computational Infrastructure的缩写,这是一个致力于"为公开文献上数学理论之数学软件而建立&q ...
- Supporting Python 3(支持python3)——常见的迁移问题
2019独角兽企业重金招聘Python工程师标准>>> 常见的迁移问题 如果你按照该建议来确保你的代码使用Python 2.7 - 3来运行没有警告,一些现在会遇到的简单错误都是可以 ...
- 关于“Cannot find any provider supporting AES/ECB/PKCS7Padding”问题的解决方案
关于"Cannot find any provider supporting AES/ECB/PKCS7Padding"问题的解决方案 参考文章: (1)关于"Canno ...
- Blockchain Meeting supporting papers
Blockchain Meeting supporting papers 文章目录 Blockchain Meeting supporting papers What is Blockchain? T ...
- JAVA——DES/ECB/PKCS7Padding加密算法[Cannot find any provider supporting DESEDE/CBC/PKCS7Padding]解决方案
基本概念 DES算法:密码体制中的对称密码体制,又被称为美国数据加密标准,是1972年美国IBM公司研制的对称密码体制加密算法. 明文按64位进行分组,密钥长64位,密钥事实上是56位参与DES运算( ...
- Supporting Multiple Screens 翻译 支持各种屏幕（上）
Supporting Multiple Screens 支持各种各样的屏幕尺寸.屏幕密度 Android runs on a variety of devices that offer differe ...
- Supporting Python 3(支持python3)——为Python 3做准备
2019独角兽企业重金招聘Python工程师标准>>> 为Python3作准备 在开始添加Python 3的支持前,为了能够尽可能地顺利过度到Python 3,你应该通过修改对2to ...
- Dialogue Summarization with Supporting Utterance Flow Modeling and Fact Regularization阅读笔记
Motivation 作者认为对话存在两个重要特性. 第一个特性:传统的文本摘要比如说新闻摘要,往往只关注新闻的前几句话,而对话摘要关注的焦点,则需要从对话的开始慢慢的转移到对话的结束,作者将这个特点 ...
- Android官方文档翻译 十二 3.Supporting Different Devices
Supporting Different Devices 支持不同设备 Dependencies and prerequisites 依赖关系和先决条件 Android 1.6 or higher A ...
最新文章
- 开发日记-20190614 克服过去
- .NET SDK-Style 项目（Core、Standard、.NET5）中的版本号
- （38）FPGA数码管驱动设计（第8天）
- Python中的命名空间是什么？
- java方法synchronized_java synchronized方法 – 它是如何工作的
- DOM技术对xml增删改查后更新源文件异常报错
- php 用pdf转html,使用PHP将HTML PDF转换为PDF
- wincc控件之FlexGrid系列(注册安装)
- UCOS操作系统——软件定时器（八）
- ubuntu查看opencv的版本
- 带网口插卡4G DTU是什么？RS485/RS232转以太网串口服务器软件怎么实现？
- OSChina 周一乱弹 —— 为单身狗准备的菜
- matlab符号表达式vpa,Matlab符号运算总结
- python大数据工程师招聘_大数据工程师是做什么的为什么招聘网上薪资都好高啊？...
- python 统计英语文档词汇出现频率，以六级真题为例
- 51单片机实战教程（34 线缆摇摆测试机设计）
- Ubuntu 桌面便签小工具-Indicator Stickynotes
- intel英特尔NUC主机bug大清除案例
- Python：对图片批量进行重命名
- 2008年度十大科技突破