argument of the maximum/minimum
argmaxf(x ) : ) x )取最大值时,x取的值
argminf(x ):f ) x取最小值时,x取的值
表示将目标函数设为最小值时的变量值
来自维基百科
In mathematics,argmax(orargmax ) standsfortheargumentofthemaximum,that is to say,thesetofpointsofthegivenargumentforwhichtion
在Words上,
isthesetofvaluesofxforwhichf(x ) has the largest value M. For example,iff ) x ) is 1|x|,thenitattainsitsmaximumvalueof1alueof1atx
Equivalently,if M is the maximum of f,thentheargmaxisthelevelsetofthemaximum 3360
ifthemaximumisreachedatasinglevalue,thenonereferstothepointastheargmax,meaningwedefinetheargmaxasapoint,notasetofpoints
(ratherthantheSingletonset (,sincethemaximumvalueofx(10x ) is 25,which happens when x=5.[note 2]
However,incasethemaximumisreachedatmanyvalues,arg max is a set of points。
Then,we have for example
sincethemaximumvalueofcos(x ) is 1,whichappensonthisintervalwhenx=0,2or4. onthewholerealline,theargmaxis { 0,2 }
argmin(orargmin ) is defined analogously。
notealsothatfunctionsdonotingeneralattainamaximumvalue,andhencewillingeneralnothaveanargmax : (nderset (x ) BBB ave x is undefined,asxisunboundedontherealline.however,bytheextremevaluetheorem (ortheclassicalcompactnessargument ),acontion