convex

convex set

check the definition in real analysis here convex set

Set is a convex set if it contains a line segment between any two of it’s points.

convex function

Function is convex function on convex set if it’s graph along any line segment in lies on or below chord connecting function values at endpoints of segment.

Def

Any local minimum of convex function on convex set is global minimum of on .

Def

Any local minimum of strictly convex function on convex set is unique global minimum of on .