## OPTIMIZATION Course

# Minimum (local)

If we are taking an interval [x,y], then the minimum on this interval is called `Minimum (local)`

(or local optimum).

The minimum is strict if we only got one if the interval (for instance, we can have two points having 0,0 the minimum for our function xxx, this minimum isn't strict).

Not tired of formulas? $x^*$ is a minimum local if we have a $\epsilon > 0$ giving us

\[ \begin{cases} x \in X \cap B(x*,\epsilon) \\ f(x*) \geq f(x) \end{cases} \] .