def

level set is set of all points for which 𝑓 has some given constant value

sublevel set

sublevel set is 𝐿𝛾={π‘₯βˆˆπ‘†:𝑓(π‘₯)≀𝛾}

Def

If a continue function 𝑓 on π‘†βŠ†β„π‘› has nonempty sublevel set and the set is closed and bounded, then 𝑓 has global minimum on 𝑆.

Def

if 𝑆 is unbounded, then 𝑓 is coercive on 𝑆 if and only if all of it’s sublevel set ate bounded.