zoukankan      html  css  js  c++  java
  • 符号arg含义

    argument of the maximum/minimum

    arg max f(x): 当f(x)取最大值时,x的取值

    arg min f(x):当f(x)取最小值时,x的取值

    表示使目标函数取最小值时的变量值
    From Wikipedia

    In mathematicsarg max (or argmax) stands for the argument of the maximum, that is to say, the set of points of the given argument for which the value of the given expression attains its maximum value:[note 1]

    underset{x}{operatorname{arg\,max}} \, f(x) := {x | forall y : f(y) le f(x)}

    In other words,

    underset{x}{operatorname{arg\,max}} \, f(x)

    is the set of values of x for which f(x) has the largest value M. For example, if f(x) is 1−|x|, then it attains its maximum value of 1 at x = 0 and only there, so underset{x}{operatorname{arg\,max}} \, (1-|x|) = {0}.


    Equivalently, if M is the maximum of f, then the arg max is the level set of the maximum:

    underset{x}{operatorname{arg\,max}} \, f(x) = f^{-1}(M) = {x | f(x) = M }

    If the maximum is reached at a single value, then one refers to the point as the arg max, meaning we define the arg max as a point, not a set of points. So, for example,

    underset{xin Bbb{R}}{operatorname{arg\,max}} (x(10-x)) = 5                     //只有一个值使函数取最大值,则arg为该值

    (rather than the singleton set {5}), since the maximum value of x(10 − x) is 25, which happens when x = 5.[note 2]

    However, in case the maximum is reached at many values, arg max is a set of points.

    Then, we have for example

    underset{x in [0,4pi]}{operatorname{arg\,max}} \, cos(x) = {0,2pi,4pi}                      //若多个值使函数取最大值,则arg为集合

    since the maximum value of cos(x) is 1, which happens on this interval when x = 0, 2π or 4π. On the whole real line, the arg max is {0, 2pi, -2pi, 4pi, dots }.

    arg min (or argmin) is defined analogously.

    Note also that functions do not in general attain a maximum value, and hence will in general not have an arg max: underset{xin Bbb{R}}{operatorname{arg\,max}}\, x is undefined, as x is unbounded on the real line. However, by the extreme value theorem (or the classical compactness argument), a continuous function on a compact interval has a maximum, and thus an arg max.                  //若无法取到最大值,无定义

     

  • 相关阅读:
    C
    C
    如何收集项目日志统一发送到kafka中?
    Jmeter压测快速体验
    实时收集Storm日志到ELK集群
    Neo4j的查询语法笔记(二)
    Logstash2.3.4趟坑之集成Redis哨兵模式
    Spring-Boot中如何使用多线程处理任务
    使用SpringBoot1.4.0的一个坑
    手动从零使用ELK构建一套搜索服务
  • 原文地址:https://www.cnblogs.com/awishfullyway/p/6074009.html
Copyright © 2011-2022 走看看