2. Unconstrained Optimization(2th)

Posted 2021-03-22 shencangzaiyunduan

2.1 Basic Results on the Existence of Optimizers

 2.1. Definition
Let $f:U->mathbb{R}$ be a function on a set $Usubseteq mathbb{R}^n$. Let $x^*in U$ be an arbitrary point, and let $B_r(x^*):={xin U:|| x-x^*||<r}$ be the open ball of radius $r$ around $x^*$. The point $x^*$ is called
-(a) a local minimizer of $f$ if

$$
f(x^*)leq f(x)
$$